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Easy Multi-Step Word Problems

Welcome to The Easy Multi-Step Word Problems Math Worksheet from the Word Problems Worksheets Page at Math-Drills.com. This math worksheet was created or last revised on 2017-04-26 and has been viewed 798 times this week and 6,742 times this month. It may be printed, downloaded or saved and used in your classroom, home school, or other educational environment to help someone learn math.

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Multi-Step Equation Worksheets

A huge collection of printable multi-step equations worksheets involving integers, fractions and decimals as coefficients are given here for abundant practice. Solving and verifying equations, applications in geometry and MCQs are included in this section for 7th grade and 8th grade students. We offer some free worksheets too!

Solving Equations Involving Integers: Level 1

Solving Equations Involving Integers: Level 1

In these 'Level 1' worksheets, solve each multi-step equation to find the value of the unknown variable. Five exclusive pdfs are here for practice.

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Solving Equations Involving Integers: Level 2

Solving Equations Involving Integers: Level 2

These 'Level 2' multi-step equations may involve a few more steps to arrive the solution than level 1. A plenty of practice worksheets are available here.

Solving Equations Involving Fractions

Solving Equations Involving Fractions

These printable worksheets have equations whose coefficients are fractions and integers. Solve each multi-step equation. Eight questions are given per worksheet.

problem solving multiple step problems practice 6 7 answers

Solving Equations Involving Decimals

In these pdf worksheets for grade 7 and grade 8, perform the basic arithmetic operation and solve the multi-step equations having decimal numbers as coefficients.

Solving Equations: Mixed Review

Solving Equations: Mixed Review

A combination of integer, fraction and decimal coefficients stands for the variable in these mixed review worksheets. Practice them all.

Equation Word Problems Worksheets

Equation Word Problems Worksheets

Read the word problems and write down the equations. Solve them in one, two or more steps to find the solution.

(30 Worksheets)

Solve and Verify the Solution

Solve and Verify the Solution

In these pdf worksheets, solve the multi-step equations and verify your solution by substituting the value of the unknown variable to the equation.

Translating Multi-Step Equation

Translating Multi-Step Equation

Translate the given phrases to algebraic equations. Three exclusive practice sheets are available here for students.

Equations in Geometry: Type 1

Equations in Geometry: Type 1

Nine geometric shapes are shown in each worksheet. Their sides are given in the form of expressions. Solve them to find the unknown variable.

Area and Perimeter - Shapes: Type 2

Area and Perimeter - Shapes: Type 2

In these printable worksheets, the area and perimeter of nine shapes are given. Use the given expressions and apply the area and perimeter formula to solve them.

Equations in Geometry: Type 3

Equations in Geometry: Type 3

A collection of word problems involving properties of shapes are given. Set up the equation and solve each multi-step equation.

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» Two-Step Equation

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Solving Multi-Step Equations: Explanations, Review, and Examples

  • The Albert Team
  • Last Updated On: February 16, 2023

Solving Multi-Step Equations: Explanations, Review, and Examples

Whether you’re new to solving multi-step equations or simply studying before that big chapter test, Albert has you covered!

This blog post will guide you through defining multi-step equations, examples of multi-step equations, and how to solve multi-step equations (including problems with fractions and words). Let’s go!

Return to the Table of Contents

What We Review

What is a multi-step equation?

Remember, an equation is a mathematical sentence that uses an equal sign, = , to show that two expressions are equal. 

We began our study of solving equations with one-step equations , then we moved on to two-step equations . (Check out those links if you need a quick refresher!) 

Now we are moving to multi-step equations . A multi-step equation is an equation that takes two or more steps to solve. These problems can have a mix of addition, subtraction, multiplication, or division. We also might have to combine like terms or use the distributive property to properly solve our equations. 

So get your mathematical toolbox out! You never know what you might see in a multi-step equation!

problem solving multiple step problems practice 6 7 answers

Examples of multi-step equations

Multi-step equations are a wide-ranging category of equations. Some can be very simple, while others become more complex. Never fear! We’re going to show you many examples of multi-step equations and how to solve these important aspects of Algebra 1. 

Here are some examples of multi-step equations: 

How to solve multi-step equations

Remember, an equation is solved when we have isolated the variable and found a value that makes the equation true. In order to solve equations, we use inverse operations to help us isolate the variable.

Order of Operations

Another mathematical concept that will help when solving multi-step equations is the Order of Operations . To use the order of operations, we must first do any operations inside grouping symbols (parentheses, brackets, etc), then exponents, then multiplication or division (whatever comes first, left to right), then finally addition or subtraction (whatever comes first, left to right). You can remember this by the acronym, PEMDAS .

A graphic showing the order of operations using the PEMDAS acronym.

Additionally, we may have to combine like terms on either side of the equation to help solve these equations. Eventually, you will create a one- or two-step equation that you will be able to solve similarly to previous problems! 

Here is an example of a multi-step equation with variables on both sides:

Solve for x in the following equation:

Since there are variables on both sides, we must eliminate the variable from one side first. I suggest moving the 4x first, as to not create a negative. 

Now we are back to a basic two-step equation.

To check you answer, you can simplify substitute 3 into the variable to see if the equation is true: 

Thus, x = 3 is the correct solution. 

Below is a short video from Mike DeVor showing more examples of solving multi-step equations:

problem solving multiple step problems practice 6 7 answers

Now that we have been introduced to Multi-Step Equations, let’s get those brain gears in motion and look at some more challenging examples!

Multi-step equations with fractions

When dealing with an equation with more than one fraction, the easiest way to solve the equation is by finding the Least Common Denominator . The least common denominator is the smallest number that can be a common denominator for a set of fractions. 

Once we find the least common denominator, we will multiply each term by this value to eliminate the fraction. Here is an example of a multi-step equation with fractions: 

Solve for y in the following equation:

The denominators above are 2, 4, 6 , therefore the least common denominator for these numbers is 12 . So we will multiply each term by 12 .

To check your answer, you can substitute 9 into the variable to see if the equation is true:

Therefore, y = 9 is the correct solution. 

Multi-step equations with distributive property

Solve for z in the following equation:

To check you answer, you can substitute 3 into the variable to see if the equation is true:

Thus, z = 3 is the correct solution.

Solve for m in the following equation:

To check you answer, you can simplify substitute -9 into the variable to see if the equation is true:

Thus, m = -9 is the correct solution.

Multi-step equation word problems

First, let’s create an equation for the situation: 

To check you answer, you can simplify substitute 15 into the variable to see if the equation is true:

Therefore, the breakeven point for Distributor A and Distributor B would be 15  pounds.

First, let’s set up an equation that models the situation:

Since each book costs the same amount, we denote this amount by the variable, c . Then we applied the \$5 coupon to each book, and finally, we will multiply the cost of each book after the coupon by 3 . 

Now, simply solve for c like any other multi-step equation: 

Therefore, each book cost \$20 before the coupon was applied.

Keys to Remember: Solving Multi-Step Equations

  • A multi-step equation is an equation that requires two or more steps to solve.
  • When solving: remember whatever you do to one side, you must do to the other.
  • To solve multi-step equations with fractions, you can multiply each term by the least common denominator to eliminate the fractions first.
  • To check the solution, simply substitute the value into the variable to see if the equation is true.
  • You can model real-life situations with an equation and solve for a correct solution.

Read these other helpful posts:

  • Solving One-Step Equations
  • Solving Two-Step Equations
  • Forms of Linear Equations
  • View ALL Algebra 1 Review Guides

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Solving Multi-Step Linear Equations

Add/Subtract Times/Divide Multi-Step Parentheses Zero/No/All Sol'n

In the previous two pages, we've looked at solving one-step linear equations; that is, equations that require one addition or subtraction, or that require one multiplication or division. However, most linear equations require more than one step in order to find their solution. What steps then should be used, and in what order?

For multi-step linear equations, we'll be using the same steps as we have previously; the only difference is that we won't be done after one step. We'll still have to do at least one more step. In what order should these steps be done? Well, that's going to vary with the equation, but there are some general guidelines which can prove helpful.

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Solving Multi-Step Equations

Solve 7 x + 2 = −54

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The variable is on the left-hand side (LHS) of the equation. It is currently multiplied by seven, and then it has a two added to it. I need to undo the "times seven" and the "plus two".

There is no rule about which "undo" operation I should do first. However, if I first divide through by 7 , I'm definitely going to create fractions. Personally, I prefer to avoid fractions if possible, so I almost always do any plus / minus before any times / divide. I might end up having to deal with fractions anyway, but at least I can put them off until closer to the end of my work.

Starting with the "plus two" first, I'll subtract two from either side of the equation. Only then will I divide through by the seven. My work looks like this:

7x + 2 = -54 -2 -2 ------------ 7x = -56 -- --- 7 7 x = -8

By doing the plus / minus first, I avoided fractions. As you can see, the answer doesn't involve fractions, so I did myself a favor by doing the dividing-through last. My solution is:

x = −8

Formatting your homework and showing your work in the manner I have done above is, in my experience, fairly universally acceptable. However (warning!), it is also a good idea to clearly rewrite your final answer at the end of each exercise, as shown (in purple) above. Don't expect your grader to take the time to dig through your work and try to figure out what you probably meant your answer to be. Format your work so as to make your meaning clear.

Solve −5 x − 7 = 108

In this equation, the variable (on the left-hand side) is multiplied by a minus five, and then a seven is subtracted from it. In hopes (as always!) of avoiding fractions, I'll add seven to either side of the equation first. Only then will I divide through by the minus five. My work looks like this:

-5x - 7 = 108 +7 +7 ------------- -5x = 115 --- --- -5 -5 x = -23

I've shown my work neatly. Now I'll clearly rewrite my solution at the end of my work:

x = −23

Solve 3 x − 9 = 33

The variable (on the left-hand side of the equation) is multiplied by a three, and then a nine is subtracted from it. I'll take care of the nine first, and then the three:

3x - 9 = 33 +9 +9 ----------- 3x = 42 -- -- 3 3 x = 14

In this case, again, my solution has no fractions:

Solve 5 x + 7 x = 72

In this equation, I have two terms on the left-hand side that contain variables. So my first step is to combine these " like terms " on the left. Then I can solve:

5 x + 7 x = 12 x

So now my equation is:

Even though it might initially have looked more complicated, this is actually a one-step equation. I'll solve by dividing through by twelve:

12x = 72 --- -- 12 12 x = 6

My answer is:

Solve 4 x − 6 = 6 x

In this equation, I've got terms with variables on either side of the equation. To solve, I need to get those variable terms all on one side of the equation.

There is no rule saying which of the two terms I should move, the 4 x or the 6 x . However, I've learned from experience that, to avoid negative coefficients on my variables, I should move the x term with the smaller coefficient. That means, in this case, that I'll subtract the 4 x from the left-hand side over to the right-hand side:

4x - 6 = 6x -4x -4x ------------- -6 = 2x

And now I have a one-step equation, which I'll solve by dividing through by two:

-6 = 2x -- -- 2 2 -3 = x

My solution is:

x = −3

In the above exercise, the variable (in my working) ended up on the right-hand side of the equation. This is perfectly okay. The variable is not "required" to end up on the left-hand side of the equation; we're just used to seeing it there. So the result " −3 =  x " is perfectly okay, and means exactly the same thing as " x  = −3 ".

However (warning!), I have heard that some instructors insist that the variable be placed on the left-hand side of the equation in the final answer . (No, I'm not making this up.) So, even though the " −3 =  x " is perfectly valid in the working, those instructors will count this as "wrong" if you leave the answer this way. If you have any doubts about your instructor's formatting preferences, ask now.

Solve 8 x − 1 = 23 − 4 x

In this equation, I've got variables on either side of the equation, and also loose numbers on either side. I need to get the variable terms on one side, and the loose numbers on the other side. Because I'd like to avoid negative coefficients on my variables, I'll be moving the smaller of the two terms; namely, the −4 x that's currently on the right-hand side. To get the loose numbers on the side opposite the variable terms, I'll be moving the −1 that's currently on the left-hand side. There is no particular "right" order for doing these steps; since they're both a matter of adding, people usually do them together in one step. I'll do the variable terms first, and then the loose numbers:

8x - 1 = 23 - 4x +4x +4x ----------------- 12x - 1 = 23 +1 +1 ------------ 12x = 24

At this point, I've got a one-step equation which requires one division to solve:

12x = 24 --- -- 12 12 x = 2

Then my answer is:

If, in the above, I'd done the first two steps at one go, it would have looked like this:

8x - 1 = 23 - 4x +4x +1 +1 +4x ----------------- 12x = 24 --- -- 12 12 x = 2

It's probably a good idea, when you're just starting out, to do each step separately. But once you get comfortable with the process (and are reliably arriving at the correct values), feel free to start combining some steps.

Solve 5 + 4 x − 7 = 4 x − 2 −  x

This equation is all kinds of messy! Before I can solve, I'll need to combine the like terms on either side of the equation:

   5 + 4 x − 7 = 4 x − 2 − x

(5 − 7) + 4 x = (4 x − 1 x ) − 2

−2 + 4 x = 3 x − 2

Now that I've simplified each side of the equation, I can do the solving.

-2 + 4x = 3x - 2 -3x -3x ----------------- -2 + 1x = -2 +2 +2 ----------------- 1x = 0

I added the (usually unstated) 1 to the variable term on the right-hand side of the original equation in order to help me keep track of what I was doing; it isn't "necessary". And it isn't expected on the final answer, which is properly stated as:

It is perfectly fine for x to have a value of zero. Zero is a valid solution. Do not say that this equation has "no solution"; it does indeed have a solution, that solution being x = 0 .

Solve 0.2 x + 0.9 = 0.3 − 0.1 x

This equation solves just like all the other linear equations I've done. It just looks worse because of the decimals. But that's easy to fix!

Whatever is the largest number of decimal places in any of the coefficients, I can multiply through on both sides by " 1 " followed by that number of zeroes. In this case, all of the decimals have one decimal place, so I'll multiply through by 10 :

10(0.2 x + 0.9) = 10(0.3 − 0.1 x )

10(0.2 x ) + 10(0.9) = 10(0.3) − 10(0.1 x )

2 x + 9 = 3 − 1 x

Now I can solve as usual:

2x + 9 = 3 - 1x +1x +1x ----------------- 3x + 9 = 3 -9 -9 ------------ 3x = -6 -- -- 3 3 x = -2

Just because the original equation had decimal places, doesn't mean that I'm stuck working with them. File this trick away for later; it'll come in handy.

x = −2

By the way, if the coefficent with the most decimal places had had two decimal places, then I'd have multiplied through on both sides of the equation by 100 ; for three decimal places, I'd have multiplied through by 1000 ; and so forth.

Solve katex.render("\\boldsymbol{\\color{green}{ \\frac{1}{4}x + 1 = \\frac{1}{6}x + \\frac{1}{2} }}", typed01);

Ick! Fractions! But, just as with the decimals in the previous exercise, I don't have to be stuck with fractions. In this case, I'll be multiplying through to "clear" the denominators, giving me a nicer equation to solve.

This is now a much nicer equation to work with. I'll continue my solution by subtracting the smaller 2 x from either side:

3x + 12 = 2x + 6 -2x -2x ------------------ 1x + 12 = 6 -12 -12 ------------------ 1x = -6

I'll remove the 1 from the variable when I write my final answer:

x = −6

You can use the Mathway widget below to practice solving a multi-step linear equation. Try the entered exercise, or type in your own exercise. Then click the button to compare your answer to Mathway's. (Or skip the widget and continue with the lesson.)

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(Clicking on "Tap to view steps" on the widget's answer screen will take you to the Mathway site for a paid upgrade.)

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Multistep Ratio Problems

New york state common core math grade 7, module 1, lesson 14.

Lesson 14 Student Outcomes Students will solve multi-step ratio problems including fractional markdowns, markups, commissions, fees, etc. Example 1: Bargains

A retail clothing store advertises the following sale: Shorts are 1/2 off the original price; pants are 1/3 off the original price, 1/4 off the original price (called the discount rate).

a. If a pair of shoes costs $40 and is advertised at 1/4 off the original price, what is the sales price? b. At Peter’s Pants Palace a pair of pants usually sells for $33.00. If Peter advertises that the store is having 1/3 off sale, what is the sale price of Peter’s pants?

Example 2: Big Al’s Used Cars

A used car sales person receives a commission of 1/12 of the sales price of the car for each car he sells. What would the sales commission be on a car that sold for $21,999? Example 3: Tax Time

As part of a marketing ploy, some businesses mark up their prices before they advertise a sales event. Some companies use this practice as a way to entice customers into the store without sacrificing their profits.

A furniture store wants to host a sales event to improve their profit margin and to reduce their tax liability before their inventory is taxed at the end of the year.

How much profit will be business make on the sale of a couch that is marked-up by 1/3 and then sold at a 1/5 off discount if the original price is $2400?

Example 4: Born to Ride

A motorcycle dealer paid a certain price for a motorcycle and marked it up by 1/5 of the price he paid. Later, he sold it for $14,000 what is the original price?

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Multi Step Equations

Multi step equations are equations that need more than two steps to solve for the variable. We use the same operation on both sides of the equation to such equations. Solving multiple step equations is sometimes complicated when compared to one step or two-step equations as they require multiple steps.

Let us see how to solve multi-step equations and the properties that we use for the same.

What are Multi Step Equations?

Multi step equations are equations that require more than one operation (applied on both sides) to solve for the required variable. Often word problems also may lead to multi step equations. They look complicated . Here are some examples of multi step equations:

  • 2 (4x - 5) = 3x - 7
  • –3 [(1/5)t + 1/3] = 9
  • 16 - (2x + 1) = (5x - 2) + 13

We already know how to solve one-step and two-step equations . We just extend the same process to solve the multi step equations as well. i.e., we use the properties of equations (like adding, subtracting, multiplying, or dividing both sides by some number/variable such that the equation is balanced) to solve the multi step equations. Let us see how to solve them.

Inverse Operations For Solving Multi-Step Equations

We solve the multi step equations by applying inverse operation on both sides to isolate the variable (making the variable alone on one side of the equation). Note that equality should not be disturbed when we apply any operation. For this, we should apply the same operation on both sides. For example, to solve x + 2 = 3 (of course, this is not a multi step equation), we should subtract 2 from both sides, then we get x + 2 - 2 = 3 - 2 which gives x = 1. Here since we are subtracting 2 from the left side, we should subtract the same number 2 from the right side as well. Wait! Why did we "subtract" 2? Because in the original equation x + 2 = 3, 2 was getting added to x, and to solve for x, we do NOT need + 2 on the left side, so we have subtracted it (as subtraction is the inverse operation of addition). Let us quickly revise the inverse operations:

  • Addition and subtraction are inverse operations of each other
  • Multiplication and division are inverse operations of each other
  • Exponents and roots are inverse operations of each other Example: square and square root are inverse operations of each other, cube and cube root are inverse operations of each other, etc).

Applying the same operation on both sides without affecting the equality is proposed by the properties of equations. Here are some examples to understand them.

Solving Multi Step Equations

To solve multi step equations we may need to apply multiple types of inverse operations one after the other (that are mentioned in the previous section). The order of applying inverse operations is very important while solving multi step equations. For example, to solve the equation 2x + 4 = 6, the first step is NOT dividing both sides by 2, rather we subtract 4 from both sides. i.e.,

2x + 4 = 6 Subtracting 4 from both sides, 2x = 2 Dividing both sides by 2, x = 1

Our ultimate aim is to get just the variable on one side of the equation. We should aim at getting the answer something like "variable = something". Here are the important steps to solve multi step equations:

  • Apply distributive property when you have a parenthesis.
  • Combine like terms (if any).
  • Collect like terms to one side of the equation. i.e., collect variable terms on the left side and the constants on the right side (or vice versa).
  • Isolate the variable by inverse operations.

solving multi step equations

Here is an example to understand these steps.

Example: -2 (x - 3) - 7 = 7x + 11

This is a multi step equation with variable on both sides.

Applying distributive property (i.e., distributing -2 to the terms inside the brackets),

-2x + 6 - 7 = 7x + 11

Combing like terms (i.e., 6 - 7 = -1),

-2x - 1 = 7x + 11

Now our aim is to collect all x terms on the left and all constant on the right.

Subtracting 7x from both sides,

-9x - 1 = 11

Adding 1 on both sides,

Our aim is fulfilled now. Now, let us divide both side by -9,

Since x is isolated, it means that we have solved the equation.

Multi Step Equations with Fractions

Sometimes, multi step equations may involve one or more fractions in them. The easiest way of solving such equations is

  • Find the LCD (Least Common Denominator) of all the denominators (of both left and right sides).
  • Multiply every term on both sides of the equation by LCD .
  • Apply inverse operations and isolate the variable.

Here is an example.

Example: Solve (1/4)t + 1/5 = (1/2)t + 5/3

The denominators are 4, 5, 2, and 3. Their LCD is 60. So multiply each term on both sides by 60.

(1/4)t × 60 + 1/5 × 60 = (1/2)t × 60 + 5/3 × 60

15t + 12 = 30t + 100

Now, the equation is free from fractions. We will proceed now. Subtracting 30t and 12 from both sides,

Dividing both sides by -15,

t = -88/15.

☛ Related Topics:

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Multi Step Equations Examples

Example 1: Solve the equation for "s": 3 (4s + 1) = 9.

We can solve the given multi step equation in two ways.

3 (4s + 1) = 9 Dividing both sides by 3, 4s + 1 = 3 Subtracting 1 from both sides, 4s = 2 Dividing both sides by 4, s = 1/2

3 (4s + 1) = 9 Distributing 3, 12s + 3 = 9 Subtracting 3 from both sides, 12s = 6 Dividing both sides by 12, s = 1/2

Answer: The solution is s = 1/2.

Example 2: Solve (1/3) x + 5 = 6x for x.

The given equation is:

(1/3) x + 5 = 6x

Multiply each term on both sides by 3 to avoid the fraction. x + 15 = 18x Let us collect the variables on one side. Subtracting x from both sides, 15 = 17x Dividing both sides by 17, x = 15/17

Answer: The solution of the given multi-step equation is x = 15/17.

Example 3: John is 5 years elder than his brother Michael. After 10 years, the sum of their ages is 35. Then how old is Michael now?

This is a multi-step equations word problem.

Let Michael is x years old. Then John's age = x + 5. After 10 years, the sum of their ages is 35. i.e.,

(x + 10) + (x + 5 + 10) = 35

Combining like terms ,

2x + 25 = 35

Subtracting 25 from both sides,

Dividing both sides by 2,

Answer: Michael is 5 years old.

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FAQs on Multi Step Equations

How do you solve multi step equations.

To solve multi step equations , aim at getting the required variable on the left side of the equation. All the other numbers/variables should be removed from the left side by using inverse operations. The inverse operation of addition is subtraction (and vice versa) and the inverse operation of multiplication is division (and vice versa).

How to Solve Multistep Equations With Variables on Both Sides?

If a multi step equation has variables on both sides, then apply inverse operations to get the variable terms on one side and constant terms on the other side. Then solve for x. For example: 3x + 5 = 7x + 6 ⇒ 3x + 5 - 7x = 6 ⇒ -4x + 5 = 6 ⇒ -4x = 6 - 5 ⇒ -4x = 1 ⇒ x = -1/4.

How to Solve Multi Step Equations With Fractions?

If a multi step equation has fractions, then we can eliminate all fractions first by multiplying each term on both sides by LCD of all denominators. Then we can just apply the inverse operations and solve for the variable.

What are the 4 Steps of Multi Step Equations?

To solve multi step equations:

  • Expand brackets by using distributive property if any.
  • Combine like terms if any.
  • Collect like terms of one type on either side.
  • Apply inverse operations to isolate the variable.

Where to Find Multistep Equations Worksheets?

We can find multi step equations worksheets by clicking here . You can get varieties of problems (both equations and word problems) by clicking on the given link.

How to Solve Multi Step Equations Word Problems?

To solve multi step equations word problems:

  • First, identify the variables with respect to the given context.
  • Frame the multi step equation by reading the problem carefully.
  • Solve it using the method that is explained on this page.

The multi step equation can also be solved directly through graph and it is often used in linear programming .

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Free Printable Multi-Step Word Problems worksheets

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Multi-Step Word Problems worksheets are an essential tool for teachers looking to challenge their students in the realm of Math. These worksheets provide a variety of Math Word Problems that require students to use critical thinking and problem-solving skills to find the solution. By incorporating multiple steps, these worksheets help students develop a deeper understanding of mathematical concepts and improve their ability to apply these concepts in real-world situations. Teachers can use these worksheets to create engaging and interactive lessons, allowing students to work individually or in groups to solve the problems. With a wide range of topics and difficulty levels, Multi-Step Word Problems worksheets cater to the diverse needs of students and can be easily adapted to suit different grade levels.

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Multi-Step Math Word Problems

What to expect in this article.

After reading this article, you will be able to analyze, process, and solve multi-step word problems . This lesson will provide help and guidance in solving these types of problems as it includes tips on how to solve a multi-step problem . There are two given examples wherein you can practice and guide your children in honing their mathematical skills. You can also read the common errors and misconceptions of students in solving multi-step problems. Furthermore, this article consists of links directed to worksheets – which you can find at the bottom of the page. 

What is a multi-step word problem?

Math word problems are a critical component of the mathematics curriculum because they help students develop their mental abilities , improve logical analysis , and stimulate creative thinking . Word problems are fun and challenging to solve because they represent actual situations that happen in our world. More so, having the ability to solve math word problems significantly benefits one’s career and personal life.

To be able to solve any math word problem , children must be familiar with the mathematics language associated with the mathematical symbols they are accustomed in order to comprehend the word problem.

A multi-step math word problem is a type of problem wherein you need to solve one or more problems first in order to get the necessary information to solve the question being asked. It usually involves multiple operations and may also involve more than one strand of the curriculum. Say, for example, a multi-step word problem involving area and perimeter may also require the application of ratio and multiplication .

How to solve multi-step word problems?

In any word problem, the true challenge is deciding which mathematical operation to use. In solving multi-step word problems, there may be two or more operations that you need to work on, and you must solve them in the correct order to be able to get the correct answer. Since word problems describe a real situation in detail, the question being asked can get lost in all the information, especially in a multi-step problem.

To solve multi-step word problems, you may follow these strategy:

  • Analyze and understand the problem. 
  • Break down each sentence of the problem and identify the clues.
  • List all the information.
  • Identify the unknown in the problem.
  • Devise a plan or identify the mathematical operations you are going to use.
  • Carry out the plan.
  • Label your final answer.

problem solving multiple step problems practice 6 7 answers

Multi-Step Word Problem #1

Step 1: Break down each sentence of the problem and identify the information needed to solve the problem.

  • The first sentence states that “Steven is reading a book that has 260 pages.” Hence, the total number of pages of that particular book is 260 .
  • The second statement says, “He read 35 pages on Monday night and 40 pages on Tuesday night.” 

Step 2: Analyze the question of the problem and find the keyword for the unknown. The last sentence of the problem, “How many pages does he has left to read?” asks us how many more pages Steven needs to read. Hence, we are going to find the number of pages he still needs to read.

Step 3: Based on the second statement, Steven read 35 pages on a Monday night and 45 pages on a Tuesday night. Hence, we will use addition in getting the total number of pages he read for 2 nights. Thus, 

35 + 40 = 75

Therefore, Steven read 75 pages in the span of two days. However, that is not the answer we are looking for. 

Step 4: Since we are asked to get the number of pages he still needs to read, the first sentence on our problem shows us that there are 260 pages in the book. Hence, we need to subtract the number of pages Steven has read from the total number of pages of the book. Thus,

260 – 75 = 185

Therefore, Steven has 185 pages left to read.

problem solving multiple step problems practice 6 7 answers

Multi-Step Word Problem #2

Jesy bought a dozen of boxes, each containing 24 highlighter pens inside. Each box costs \$8. Jesy repacked five of these boxes into packages of six highlighters each and sold them for \$3 per package. She sold the rest of the highlighters at the price of three pens for \$2. How much profit did Jesy make?

  • The statement, “Jesy bought a dozen of boxes , each containing 24 highlighter pens inside,” tells us that there are a dozen of boxes that contains 24 highlighters. A dozen means there are 12 boxes . 
  • The second sentence, “Each box costs \$8”, means Jesy bought 12 boxes at \$8 each . 
  • “Jesy repacked five of these boxes into packages of six highlighters each and sold them for \ $3 per package ” means that Jesy separated 5 boxes from the original 12 boxes to be repacked at a package of six, which was sold at \$3 each. 
  • “She sold the rest of the highlighters at the price of three pens for \$2 ” means that Jesy sold the remaining highlighters and bundled it for 3 pens for \$2.

Step 2: Analyze the question of the problem and find the keyword. The last sentence of the problem, “How much profit did Jesy make?” asks us how much profit Jesy earned after repacking the highlighter pens. Profit is defined as the amount earned minus the amount spent to buy the highlighters. 

Step 3: Based on the first statement, Jesy bought 12 boxes containing 24 highlighters. The follow-up statement that says, “Each box costs \$8” refers to the price of each box. In this particular statement, we can find the total expenditures of Jesy for the highlighter pens by simply multiplying the total number of boxes to \$8. Hence, 

12 x \$8 = \$96

This means that Jesy spent \$96 to buy all the highlighters. However, that is not the question being asked. Hence, we need to work on the follow-up statements and find more clues to get Jesy’s profit in selling highlighters. 

Step 4: The next statement says that “Jesy repacked five of these boxes into packages of six highlighters each and sold them for \$3 per package” means that Jesy separated 5 boxes from the dozen to be repacked at a package of six, which was sold at \$3 each. Based on this statement, we need to do three things:

  • Find the total number of highlighters she got from separating 5 boxes;
  • Find the total number of packages she made by repacking it by 6; and
  • Find how much money she made by selling the sets of 6 at \$3.  

Step 5: To find the total number of highlighters she got from separating 5 boxes, we simply multiply 5 by the number of highlighters inside the box. Based on the first statement, each box contains 24 highlighters. Hence,

5 x 24 = 120

This means Jesy repacked a total of 120 highlighter pens.

Step 6: To find the total number of packages she made by repacking 120 highlighter pens by 6, we will divide 120 by 6. Thus,

So, she was able to make 20 sets of 6 highlighter pens. 

Step 7: The next thing we need to do is find how much money she made by selling the sets of 6 by \$3. This can be done by multiplying 20 sets by \$3. Hence,

20 x \$3 = \$60

Thus, Jesy made \$60 from the 20 sets of 6 highlighter pens.

Step 8: The third sentence, “She sold the rest of the highlighters at the price of three pens for \$2” means that Jesy sold the remaining highlighters and bundled it for 3 pens for \$2. From this statement, we need to work on four things first:

  • Find the remaining number of boxes; 
  • Find the total number of highlighter pens she repacked;
  • Find the number of sets she repacked by making sets of 3; and
  • Find how much money Jesy made by selling packs of 3 at \$2. 

Step 9: To find the remaining number of boxes, we need to go through some of the problem statements. Based on the first statement, we have 12 boxes, then 5 boxes were separated to make a highlighter set of 6. Hence, we will subtract 5 from 12. 

So, we still have 7 remaining boxes.

Step 10: To find the total number of highlighter pens she repacked, we need to multiply the remaining 7 boxes to the number of highlighter pens inside the box. Going back to the information we already have, we know that there are 24 highlighter pens inside a box. Thus, 

7 x 24 = 168

This means Jesy repacked a total of 168 highlighter pens. 

Step 11: Find the number of sets Jesy made by repacking 168 highlighter pens by 3. This can be done by dividing 168 by 3. Hence,

Thus, Jesy was able to make 56 sets of 3 highlighter pens. 

Step 12: Determine how much money Jesy made by selling each set for \$2. Hence, 

56 x \$2 = \$112

This means Jesy made \$112 by selling 3 highlighter pens for \$2. 

Step 13: The question asks us to determine the profit Jesy made by selling the highlighter pens. In order to find the profit, we need the information of:

  • How much did Jesy spend on the highlighter. In Step 3, we found out that she paid \$96 on buying all the highlighter pens. 
  • How much money does Jesy make on selling packs of 6 highlighters for \$3. In Step 7, we already know that she made \$60; and
  • How much money does Jesy make on selling sets of 3 highlighter pens for \$2. In Step 12, we found out that she made \$112.

Step 14: Before getting the profit Jesy made, we need to know the total money Jesy made in selling the highlighters. Hence, we will simply add the money of \$60 and \$112. Thus,

\$60 + \$112 = \$172

However, \$172 is not the profit Jesy made. This is just the money she was able to make in selling the highlighter pens.

Step 15: Lastly, we will subtract the money Jesy spent on buying the highlighters from the money she made by selling it to find the profit. Thus, 

\ $172 – \$96 = \$76

Therefore, Jesy made a profit of \$76 by selling the highlighter pens.

You can tell that there are lots of things to remember with a multi-step word problem, even when the problem itself is relatively easy. But that’s what makes these problems challenging: you get to use both sides of your brain – your logical math skills and your verbal language skills. That’s why they are often more fun to do than problems that are just numbers without the details and context that word problems give you. The better you understand how to solve them, the more fun they are to solve. 

What are the common errors in solving multi-step word problems?

Mathematical word problems can be challenging to solve. To obtain the correct answer, children must read the words and carefully analyze the problem, determine the appropriate math operation, and then perform the calculations correctly. An error in working on one of the steps may result in a wrong answer. 

Here’s a list of some errors students make when solving multi-step word problems:

  • The most common error of students is stopping at one process if they solve one problem. Consider the same word problem about Steven. 

“Steven is reading a book that has 260 pages. He read 35 pages on Monday night and 40 pages on Tuesday night. How many pages does he has left to read?” 

Most students recognize that they need to add 35 and 40 together to get the total number of pages Steven has read so far. Most errors occur when students stop at one process. Adding 35 + 40 will tell you that Steven has read 75 pages so far, but if we go back to the question you are being asked, you will notice that 75 pages are not the answer you are being asked. Thus, we still need to take another step to get there. Steven has read 75 pages so far, but the questions asked us to solve the number of pages he has left to read. Hence, subtracting 75 from the total number of pages of the book makes much more sense. 

  • Students get confused with the mathematical operation to use. Even if children are strong readers, they may struggle to pick up on clues in word problems. These clues are phrases that instruct children on how to solve a problem, such as adding or subtracting. The children are then required to convert these phrases into a number sentence in order to solve word problems.

How to teach multi-step problems to children?

There are certain activities or practices that you can try with your child in order to develop their skills in solving multi-step problems. 

  • The first and most important skill in working with multi-step is being able to understand the problem clearly. Hence, practicing your child in slowly reading and visualizing problems is the first step in implementing our effective reading comprehension strategies.
  • Practice your child in recognizing mathematics terms and vocabulary that are used in word problems. There are keywords or clues that we can easily spot in a word problem if we familiarize ourselves with these mathematical terms. 

Let’s look at the sample words related to addition, subtraction , multiplication, and division.

However, some English words can sometimes be confusing as they may mean differently depending on the context. 

Let’s look at the table below:

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"Multi-Step Math Word Problems". Helping with Math , https://helpingwithmath.com/multi-step-math-word-problems/. Accessed 20 February, 2024.

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COMMENTS

  1. Multistep Worksheets

    The multi-step word problems worksheets are the best way to help students practice their skills in solving complex math problems. Our worksheets are the best on the internet and they are completely free to use.

  2. Multi-Step Equations Practice Problems with Answers

    Answer 4) Solve the multi-step equation for [latex]\large {k} [/latex]. [latex] {\Large { {6k + 4} \over 2}} = 2k - 11 [/latex] Answer 5) Solve the multi-step equation for [latex]\large {x} [/latex]. [latex] - \left ( { - 8 - 3x} \right) = - 2\left ( {1 - x} \right) + 6x [/latex] Answer

  3. Easy Multi-Step Word Problems

    Easy Multi-Step Word Problems News Welcome to The Easy Multi-Step Word Problems Math Worksheet from the Word Problems Worksheets Page at Math-Drills.com. This math worksheet was created or last revised on 2017-04-26 and has been viewed 2,161 times this week and 5,822 times this month.

  4. Multi-step equations review (article)

    Step 4: 5/3b + 5 = 20. Subtract 5 from both sides of the equation to cancel out 5. Step 5. divide 5/3 to 15. Keep change Flip Keep the fraction change the division sign to multiplication and flip the second fraction (example 2/3 to 3/2). So, 5/3 to 3/5 and multiply both sides of the equation, lastly, your answer is 4.

  5. Two-Step Equations Practice Problems with Answers

    1) Solve the two-step equation for [latex]g [/latex]. [latex]2g - 4 = 6 [/latex] Answer 2) Solve the two-step equation for [latex]x [/latex]. [latex]2x + 15 = - 3x [/latex] Answer 3) Solve the two-step equation for [latex]k [/latex]. [latex] {\Large { {k \over 4}}} - 7 = - 5 [/latex] Answer 4) Solve the two-step equation for [latex]m [/latex].

  6. Multi-step word problems with whole numbers

    Course: 4th grade > Unit 5 Lesson 8: Multi-step word problems 2-step estimation word problem Represent multi-step word problems using equations Multi-step word problems with whole numbers Google Classroom After collecting eggs from his chickens, Dale puts the eggs into cartons to sell. Dale fills 15 cartons and has 7 eggs left over.

  7. Multi-Step Equation Worksheets

    In these pdf worksheets, solve the multi-step equations and verify your solution by substituting the value of the unknown variable to the equation. Download the set Translating Multi-Step Equation Translate the given phrases to algebraic equations. Three exclusive practice sheets are available here for students.

  8. Solving Multi-Step Equations: Review and Examples

    Keys to Remember: Solving Multi-Step Equations. A multi-step equation is an equation that requires two or more steps to solve. When solving: remember whatever you do to one side, you must do to the other. To solve multi-step equations with fractions, you can multiply each term by the least common denominator to eliminate the fractions first.

  9. PDF Name 6-7 Problem Solving: Multiple-Step Problems

    Problem Solving: Multiple-Step Problems Write and answer the hidden question. Then solve. 1. Gloria talked on her cell phone for 320 minutes the first ... Explain how you found your answer. Practice 6-7 MTH12_ANC5_TRM_P06_07.indd 1 2/25/11 5:50 AM. Title: Scott Foresman Addison Wesley, enVision Math ...

  10. Solving Multi-Step Linear Equations

    As you can see, the answer doesn't involve fractions, so I did myself a favor by doing the dividing-through last. My solution is: x = −8. ... You can use the Mathway widget below to practice solving a multi-step linear equation. Try the entered exercise, or type in your own exercise. Then click the button to compare your answer to Mathway's.

  11. Multistep Ratio Problems

    a. If a pair of shoes costs $40 and is advertised at 1/4 off the original price, what is the sales price? b. At Peter's Pants Palace a pair of pants usually sells for $33.00. If Peter advertises that the store is having 1/3 off sale, what is the sale price of Peter's pants? Example 2: Big Al's Used Cars

  12. Free Printable Multi-Step Word Problems Worksheets for 6th Grade

    Multi-Step Word Problems: Discover a collection of free printable math worksheets for Grade 6 students, designed to help them master solving complex problems through a series of smaller, manageable steps. Empower your teaching with Quizizz! grade 6 Multi-Step Word Problems Multi-Step Word Problems 10 Q 5th - 6th Multi Step Word Problems 10 Q

  13. Multi Step Equations

    Here are some examples of multi step equations: 2 (4x - 5) = 3x - 7. -3 [ (1/5)t + 1/3] = 9. 16 - (2x + 1) = (5x - 2) + 13. We already know how to solve one-step and two-step equations. We just extend the same process to solve the multi step equations as well. i.e., we use the properties of equations (like adding, subtracting, multiplying, or ...

  14. Mathway

    Free math problem solver answers your algebra homework questions with step-by-step explanations.

  15. Multi-step ratio and percent problems (article)

    In other words, 150/20 is 7.5 so we already have half of the ratio (The answer must be an equivalent ratio to 3 : 20). __:150. To get the last half of the answer, we must multiply 7.5 by 3 because we already found out that 150/20 is 7.5. 3 x 7.5 is 22.5 so the answer is 22.5 : 150. Hope this helps!

  16. Multiple-Step Word Problem Worksheets

    Basic (Grades 2 - 3) Multiple Step, Basic #1 FREE Solve each of the multi-step word problems on this page. Problems contain basic numbers of 20 or less. Each problem can be solved without knowledge of multiplication or division. 2nd and 3rd Grades View PDF Multiple Step, Basic #2

  17. Free Math Worksheets

    Khan Academy's 100,000+ free practice questions give instant feedback, don't need to be graded, and don't require a printer. Math Worksheets. Khan Academy. Math worksheets take forever to hunt down across the internet. Khan Academy is your one-stop-shop for practice from arithmetic to calculus. Math worksheets can vary in quality from ...

  18. PDF Word Problem Practice Workbook

    for Glencoe Math Connects, Course 1.The answers to these worksheets are available at the end of each Chapter Resource Masters booklet as well as in your Teacher Wraparound Edition interleaf pages.

  19. Free Printable Multi-Step Word Problems worksheets

    Multi-Step Word Problems worksheets are an essential tool for teachers looking to challenge their students in the realm of Math. These worksheets provide a variety of Math Word Problems that require students to use critical thinking and problem-solving skills to find the solution. By incorporating multiple steps, these worksheets help students ...

  20. Multi-Step Math Word Problems

    To solve multi-step word problems, you may follow these strategy: Analyze and understand the problem. Break down each sentence of the problem and identify the clues. List all the information. Identify the unknown in the problem. Devise a plan or identify the mathematical operations you are going to use. Carry out the plan.

  21. Represent multi-step word problems using equations

    Choose 1 answer: 3 × 6 × ( 4 + 3) = p A 3 × 6 × ( 4 + 3) = p ( 4 × 6) + ( 3 × 6) × 3 = p B ( 4 × 6) + ( 3 × 6) × 3 = p ( 4 × 6) + ( 3 × 6) + ( 3 × 6) = p C ( 4 × 6) + ( 3 × 6) + ( 3 × 6) = p Stuck? Loading... Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more.

  22. Solving Multi Step Equations Practice Flashcards

    Study with Quizlet and memorize flashcards containing terms like x = 4, x = 5, x = 3 and more.

  23. PDF Name Practice Problem Solving: Multiple-Step Problems

    Problem Solving: Multiple-Step Problems Write and answer the hidden question or questions ... your answer in a complete sentence. 5. What are hidden questions and why are they important when ... Jeans $29.95 for 1 pair OR 2 pairs for $55.00 T-shirts $9.95 for 1 OR 3 T-shirts for $25.00 Storewide Sale Practice 7-7. Title: Scott Foresman Addison ...