algebra solving two step equations worksheet

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Two-Step Equation Worksheets

Two-step equation worksheets have a huge collection of printable practice pages to solve and verify the equations involving integers, fractions and decimals. Also, a number of exercise pdfs on translating two-step equations, MCQs and word problems based on geometric shapes are given here for additional practice for 7th grade and 8th grade students. Some of them are offered free of cost!

Solving Two-Step Equations involving Whole Numbers

Kick into gear solving single-variable two-step equations involving positive coefficients with this practice set! Rearrange the equations to make the variable the subject, and solve for its whole-number value.

Solving Equations involving Integers

In these worksheets solve the two-step equations with integer coefficients. Numerous worksheets are available for practice.

Solving Equations involving Fractions

Solve the equations which have fractions as their coefficients. Arrive the solution to the equations in just two steps.

Solving Equations involving Decimals

Decimal coefficients are included in these printable two-step equation worksheets. Solve these equations to get the value of the unknown.

Solving Equations: Mixed Review

Solve these mixed equations which involve fractions, integers and decimals. Each pdf two-step equation worksheet has ten problems for a thorough practice.

Equation Word Problems Worksheets

Utilize this set of worksheets to guide students of grade 7 and grade 8 to solve an array of diligently prepared equation word problems.

(15 Worksheets)

Solve and Verify the Solution

In these 12 worksheets solve each two-step equation to find the unknown. Substitute the value of the variable in the given equation to verify the solution.

Multiple Choice Questions

Identify the correct two-step equation or value from the given multiple responses. Each pdf worksheet has eight questions for practice.

Translating Two-Step Equation

In these printable worksheets, translate the given phrases and/ or sentences into two-step equation.

Find me! Solve these interesting problems following the given hints. Ex. If you add 7 to three times of me, you get 34. What number am I?

Equations in Geometry: Type 1

The lengths of the sides of geometric figures are given in the form of expressions. Use the given inputs to find the value of the unknown variables.

Equations in Geometry: Type 2

The properties of the geometric shapes are the clues to solve these word problems. Figure out the two-step equation from the given expressions to find the value of the unknown.

Related Worksheets

» One-step Equation

» Multi-step Equation

» Equation Word Problems

» Translating Phrases

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Home > Math Worksheets > Algebra Worksheets > Two Step Equations

Two step math equations are algebraic problems that require you to make two moves to find the value of the unknown variable. For example, using the equation 3x + 5 = 11 we will need to perform two steps to find the value of x. The first step would be to get the constant values of the equation by themselves. In this case 5 and 11 are our constants. We can always perform any operation to the equation as long as we perform the same operation to both sides of the equation. If we want to get the 5 and 11 together, we can perform the opposite operation that is already taking place with one of them. If we were to subtract 5 from both sides, we would be left with 3x = 6. That is step one. For step two we need to get rid of the 3 that is next to the variable. To undo multiplication, we can divide. If we were to divide both sides by 3, we would be left with x = 2. When we start out with algebraic equations, most teacher prefer to name the unknown variable x and stay consistent with its use. Equations of lines often are most frequently solved in two steps.

In this section, your students will work on solving for two variables in algebraic expressions and graphing the results. This set of worksheets introduces your students to the concept of solving for two variables, and provides examples, short practice sets, longer sets of questions, and quizzes. In everyday math, in the real world, a survey of daily tasks of over 1,200 was issued by UMASS. They found that two-step math problems were the most common mathematical tasks people were performing. Utilize these worksheets to demonstrate how to solve two step problems. Students will learn how to create equations from number sentences and solve them.

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Print two step equations worksheets, click the buttons to print each worksheet and associated answer key., solving two step equation problems worksheet 1.

Solve for x in the following 12 problems. Example: 2x + 4 = 12

Worksheet 2

Remember to flip the symbol of the constant that has an operation first. Example: 7x + 4 = 46

Two Step Problems Worksheet 1 (contains negatives)

Do not let the negative value throw you off the scent of the answer. Example: - 4x + 4 = - 12

Worksheet 2 (contains negatives)

You can reorder the problem before you start working on it. Example: - 3 + 7x = 4

Worksheet 3 (contains negatives)

Solve for x in the following 12 problems. Example: 3x + 4 = - 8

More Basic Worksheet 4

The arrange of values is the key here. Example: 5 - 3x = 8

Worksheet 5

See how fast you can complete all of these problems. Example: 3x + 4 = 19

Worksheet 6

See if you can start with the variable first. It is a good way to make sure you master this. Example: 3 + 2x = 17

Two Step Problems Worksheet 7

Solve for x in the following 12 problems. Example: 7 + 2x = 19

Worksheet 8

More practice to make sure you know what you are doing. Example: 6x + 1 = 13

Decimals- Meet the Skill

Learn how to solve the problem: x/2 + 3.5 = 21 Check by substituting your solution to the equation.

Try the Skill

Write an equation and solve for this number sentence: "When a number is divided by 5 and the result added to 35, the result is 105."

Practice the Skill

Solve the equations. Check by substituting your solution to the equation. Example: 9 = a/4+ 4

Practice the Skill Twice

Write an equation and solve for the following 10 sentences.

Show the Skill

These turn up the heat and are more difficult. Example: -13 = -5x + 7

Setup Equations Warm Up

Write an equation and solve for the following 3 sentences.

Meet the Skill

Define the variable, write the equation and solve it: "Three more than two times a number is forty-three."

Where is the variable? Create an equation and solve it: "Two less than a number divided by 5 is eight."

For the following 10 problems locate the unknown variable and make an equation. Oh yeah, solve it too! Example: "Seven less than a number divided by 3 is five."

What final value is being described by the math sentences? Example: "Two more than a number divided by 3 is eleven."

This problems are great to help you start thinking algebraically.

Why not read the problem and take an educated guess before you break down the algebra?

Writing Two-Step Equations - Lesson

We show you how to complete all the following problems.

Practice Worksheet 1

You don't always need to use the variable x. Try using something more abstract to make it interesting.

It is always a good idea to write the components of the equation in the same order as the sentence.

Review Sheet

This walks you through all the steps you need to know.

Practice this skill by completing the 6 problems on this sheet.

See how well you know this topic.

"Do Now"

This is designed to be used as a whole class activity.

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• 2 step equations

Algebra with 2 step equations

Simplify and solve.

These algebra worksheets provide practice in simplifying and solving 1-variable algebraic equations. Students should be encouraged to show their work in stepwise fashion.

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Two Step Equations Worksheets

The free printable worksheets belonging to this post need to be solved in just two steps- no more, no less. They are a combination of number and word problems.

• One and Two Step Equations Worksheets

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Algebraic Equations (Two-Step)

Practice solving two-step algebraic equations with these printable worksheets and task cards. Common Core Standard: 7.EE.B.4

Level: Basic Positive Whole Numbers

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Intermediate Level: Positive & Negative Integers

Advanced Level: Decimals, Exponents, & Parenthesis

If two-step equations are too advanced, go down a level and use these single-step equation resources.

We have a variety of algebra and pre-algebra topics for teaching students about independent/dependent variables, expressions, equations, and inequalities.

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Two Step Equations Worksheets

Two-step math equations are algebraic problems that require you to make two moves to find the value of the unknown variable. Hence, in the two-step equations worksheets, students will learn the concept of solving for two variables, the different ways of solving two variables in algebraic expressions, and graphing the results; equations involve fractions, integers, and decimals.

Benefits of Two-Step Equations Worksheets

Students can benefit from the two-step equations worksheets by learning how to translate two-step equations, MCQs, and word problems based on geometric shapes. These math worksheets come along with an answer key that provides a step-wise understanding for the students while practicing problems. Thus, students learn the solution at every step instead of memorizing the solution. Two-step equations worksheets also deal with the logical and reasoning aspect of mathematics and help students in real life as well.

Download Two Step Equations Worksheet PDFs

Students can download the PDF format of the two-step equations worksheets online for free to score well in exams.

☛ Check Grade wise Two Step Equations Worksheets

• 7th Grade Two-Step Equations Worksheets

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Two Step Equations Worksheets

The first major leap forward for students in prealgebra is working with equations that require multiple steps to solve. When an equation is presented to you, it is balanced meaning that both sides are equal. You can easily rearrange any equation by simply performing the operation of your choice. You just need to make sure to process that operation on both sides of the equal symbol. Whatever you decide to do to one side, will be done to the other. In most cases we are simply trying to get a variable by itself and determine what it is equal to. The most commonly used variable is the letter “x”. These worksheets and lessons help students learn how to manage problems that involve solving equations in at least two steps.

Aligned Standard: 7.EE.B.3

• Solve For X Step-by-Step Lesson - Two thumbs up if you get this one. You get two either way!
• Guided Lesson - Play through on these. Make sure to get rid of the constant first.
• Guided Lesson Explanation - In some cases, I made two steps into three steps.
• Independent Practice - I used all numbers under 20 in the operations to make sure basic operations don't trip you up.
• Matching Worksheet - Find the value of the variables in all cases.
• Practice Worksheet Pack - You will find five practice worksheets here.
• Write the Equation Worksheet Pack - We give you the words. We want the integers in return.
• Two Step Equations in Words Lesson Practice Sheet - This one was written well. I think I'm on version 30 of this.
• Two Step Equations in Words Worksheet - Now you not only need to write the equation, but solve it too.
• Answer Keys - These are for all the unlocked materials above.

Homework Sheets

Start by getting x by itself. The next step is to take a sentence and turn into a math sentence that is then solvable.

• Homework 1 - In order to get x on the left side we have to remove 4 using addition.
• Homework 2 - Write the sentence as an equation and solve it. Four less than a number divided by 3 is six.
• Homework 3 - For the first step, in order to get x on the left side we have to remove 12 using subtraction.

Practice Worksheets

The sentence based problems really give many students trouble.

• Practice 1 - It is always good to start with numbers that have no variables attached to them.
• Practice 2 - In the second step we will remove the coefficient using division. The opposite of multiplication is division.
• Practice 3 - Write the sentences as equations and solve.

Math Skill Quizzes

Remind students to combine like terms as much as possible and then proceed from there.

• Quiz 1 - Write the sentences as equations and solve. You are basically trying to represent what is presented with numbers and symbols.
• Quiz 2 - Solve for p: 6p + 2p = 72. There are some single steps in here too to allow for some confidence.
• Quiz 3 - You will find you deal a lot with negative values here. Just remember to counter the operations.

How to Approach Two-Step Equations

When you start to learn algebra, it gets more complicated every step of the way. Nonetheless, after learning a single-step equation in which you only have to switch numbers to the other side of the relational operator. For instance, when you have an equation like x + 3 = 0, you need to subtract 3 (since it's the same number on the left-hand-side) on both sides to have an equation x + 3 - 3 = 0 - 3. The answer will be x = -3. However, to solve the two-step equation, we have to learn one more single step. Let's learn it in the form of an example.

For example, we will take the equation 3x + 5 = 65. The entire goal is to get the variable (x) by itself.

The first step, in this case, will be to subtract 5 from both sides of the relational sign (3x + 5 – 5) = (65 – 5).

The result is 3x = 60; however, you haven't found the value of x alone. There is a coefficient attached to x.

In such circumstances, you need to divide with the same number as the coefficient attached to the variable. Therefore, we will divide both sides with 3. 3x / 3 = 60 / 3. So x = 20.

It is all about determining what operations are in play and then just drop the opposites to cancel them out, as you have seen in our example.

The Two Steps You Need to Solve These Problems

These problems can seem much more reasonable when you put them into perspective and think in this manner when tackling them:

1) Start by countering the math operations that are presented to you. Just remember that addition and subtraction will counter one another. Multiplication and division are adversaries as well. Whatever operation you choose to use to create balance, just use the same operation on both sides of the equation and you are all set. This will help you tip the scales in your favor.

2) The last step is just to get the variable by itself. This will again require you to counter the operations that are in place, and you are good to go.

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Welcome to the Algebra worksheets page at Math-Drills.com, where unknowns are common and variables are the norm. On this page, you will find Algebra worksheets mostly for middle school students on algebra topics such as algebraic expressions, equations and graphing functions.

This page starts off with some missing numbers worksheets for younger students. We then get right into algebra by helping students recognize and understand the basic language related to algebra. The rest of the page covers some of the main topics you'll encounter in algebra units. Remember that by teaching students algebra, you are helping to create the future financial whizzes, engineers, and scientists that will solve all of our world's problems.

Algebra is much more interesting when things are more real. Solving linear equations is much more fun with a two pan balance, some mystery bags and a bunch of jelly beans. Algebra tiles are used by many teachers to help students understand a variety of algebra topics. And there is nothing like a set of co-ordinate axes to solve systems of linear equations.

Most Popular Algebra Worksheets this Week

Properties and Laws of Numbers Worksheets

The commutative law.

The commutative law or commutative property states that you can change the order of the numbers in an arithmetic problem and still get the same results. In the context of arithmetic, it only works with addition or multiplication operations , but not mixed addition and multiplication. For example, 3 + 5 = 5 + 3 and 9 × 5 = 5 × 9. A fun activity that you can use in the classroom is to brainstorm non-numerical things from everyday life that are commutative and noncommutative. Putting on socks, for example, is commutative because you can put on the right sock then the left sock or you can put on the left sock then the right sock and you will end up with the same result. Putting on underwear and pants, however, is noncommutative.

The Associative Law

The associative law or associative property allows you to change the grouping of the operations in an arithmetic problem with two or more steps without changing the result. The order of the numbers stays the same in the associative law. As with the commutative law, it applies to addition-only or multiplication-only problems. It is best thought of in the context of order of operations as it requires that parentheses must be dealt with first. An example of the associative law is: (9 + 5) + 6 = 9 + (5 + 6). In this case, it doesn't matter if you add 9 + 5 first or 5 + 6 first, you will end up with the same result. Students might think of some examples from their experience such as putting items on a tray at lunch. They could put the milk and vegetables on their tray first then the sandwich or they could start with the vegetables and sandwich then put on the milk. If their tray looks the same both times, they will have modeled the associative law. Reading a book could be argued as either associative or nonassociative as one could potentially read the final chapters first and still understand the book as well as someone who read the book the normal way.

Inverse relationships with one blank

Inverse relationships worksheets cover a pre-algebra skill meant to help students understand the relationship between multiplication and division and the relationship between addition and subtraction.

Inverse relationships with two blanks

Missing Numbers or Unknowns in Equations Worksheets

Missing numbers in equations worksheets in three types: blanks for unknowns, symbols for unknowns and variables for unknowns.

Missing Numbers Worksheets with Blanks as Unknowns

In these worksheets, the unknown is limited to the question side of the equation which could be on the left or the right of equal sign.

Missing Numbers Worksheets with Symbols as Unknowns

Equalities with addition on both sides of the equation and symbols as unknowns

Missing numbers worksheets with variables as unknowns

Solving Simple Linear Equations

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Using the distributive property.

The distributive property is an important skill to have in algebra. In simple terms, it means that you can split one of the factors in multiplication into addends, multiply each addend separately, add the results, and you will end up with the same answer. It is also useful in mental math, and example of which should help illustrate the definition. Consider the question, 35 × 12. Splitting the 12 into 10 + 2 gives us an opportunity to complete the question mentally using the distributive property. First multiply 35 × 10 to get 350. Second, multiply 35 × 2 to get 70. Lastly, add 350 + 70 to get 420. In algebra, the distributive property becomes useful in cases where one cannot easily add the other factor before multiplying. For example, in the expression, 3(x + 5), x + 5 cannot be added without knowing the value of x. Instead, the distributive property can be used to multiply 3 × x and 3 × 5 to get 3x + 15.

Evaluating algebraic expressions

Exponent Rules and Properties

Practice with basic exponent rules.

As the title says, these worksheets include only basic exponent rules questions. Each question only has two exponents to deal with; complicated mixed up terms and things that a more advanced student might work out are left alone. For example, 4 2 is (2 2 ) 2 = 2 4 , but these worksheets just leave it as 4 2 , so students can focus on learning how to multiply and divide exponents more or less in isolation.

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Linear equations worksheets including simplifying, graphing, evaluating and solving systems of linear equations.

Translating algebraic phrases in words to algebraic expressions

Knowing the language of algebra can help to extract meaning from word problems and to situations outside of school. In these worksheets, students are challenged to convert phrases into algebraic expressions.

Simplifying linear expressions (combining like terms)

Combining like terms is something that happens a lot in algebra. Students can be introduced to the topic and practice a bit with these worksheets. The bar is raised with the adding and subtracting versions that introduce parentheses into the expressions. For students who have a good grasp of fractions, simplifying simple algebraic fractions worksheets present a bit of a challenge over the other worksheets in this section.

Rewriting linear equations

Determining linear equations from slopes, y-intercepts, and points

Linear Equation Graphs

Graphing linear equations and reading existing graphs give students a visual representation that is very useful in understanding the concepts of slope and y-intercept.

Solving linear equations with jelly beans is a fun activity to try with students first learning algebraic concepts. Ideally, you will want some opaque bags with no mass, but since that isn't quite possible (the no mass part), there is a bit of a condition here that will actually help students understand equations better. Any bags that you use have to be balanced on the other side of the equation with empty ones.

Probably the best way to illustrate this is through an example. Let's use 3 x + 2 = 14. You may recognize the x as the unknown which is actually the number of jelly beans we put in each opaque bag. The 3 in the 3 x means that we need three bags. It's best to fill the bags with the required number of jelly beans out of view of the students, so they actually have to solve the equation.

On one side of the two-pan balance, place the three bags with x jelly beans in each one and two loose jelly beans to represent the + 2 part of the equation. On the other side of the balance, place 14 jelly beans and three empty bags which you will note are required to "balance" the equation properly. Now comes the fun part... if students remove the two loose jelly beans from one side of the equation, things become unbalanced, so they need to remove two jelly beans from the other side of the balance to keep things even. Eating the jelly beans is optional. The goal is to isolate the bags on one side of the balance without any loose jelly beans while still balancing the equation.

The last step is to divide the loose jelly beans on one side of the equation into the same number of groups as there are bags. This will probably give you a good indication of how many jelly beans there are in each bag. If not, eat some and try again. Now, we realize this won't work for every linear equation as it is hard to have negative jelly beans, but it is another teaching strategy that you can use for algebra.

Solving linear equations

Despite all appearances, equations of the type a/ x are not linear. Instead, they belong to a different kind of equations. They are good for combining them with linear equations, since they introduce the concept of valid and invalid answers for an equation (what will be later called the domain of a function). In this case, the invalid answers for equations in the form a/ x , are those that make the denominator become 0.

Linear Systems

Solving systems of linear equations.

Solving systems of linear equations by graphing

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Quadratic expressions and equations worksheets including multiplying factors, factoring, and solving quadratic equations.

Simplifying quadratic expressions (combining like terms)

Adding/Subtracting and Simplifying quadratic expressions

Multiplying factors of quadratic expressions

Factoring quadratic expressions

The factoring quadratic expressions worksheets in this section provide many practice questions for students to hone their factoring strategies. If you would rather worksheets with quadratic equations, please see the next section. These worksheets come in a variety of levels with the easier ones are at the beginning. The 'a' coefficients referred to below are the coefficients of the x 2 term as in the general quadratic expression: ax 2 + bx + c. There are also worksheets in this section for calculating sum and product and for determining the operands for sum and product pairs.

Whether you use trial and error, completing the square or the general quadratic formula, these worksheets include a plethora of practice questions with answers. In the first section, the worksheets include questions where the quadratic expressions equal 0. This makes the process similar to factoring quadratic expressions, with the additional step of finding the values for x when the expression is equal to 0. In the second section, the expressions are generally equal to something other than x, so there is an additional step at the beginning to make the quadratic expression equal zero.

Solving Quadratic equations that Equal Zero (e.g. ax² + bx + c = 0)

Solving Quadratic equations that Equal an Integer (e.g. ax² + bx + c = d)

Other Polynomial and Monomial Expressions & Equations

Factoring non-quadratic expressions worksheets with various levels of complexity.

Simplifying polynomials that involve addition and subtraction

Simplifying polynomials that involve multiplication and division

Simplifying polynomials that involve addition, subtraction, multiplication and division

Factoring expressions that do not include a squared variable

Factoring expressions that always include a squared variable

Factoring expressions that sometimes include squared variables

Multiplying polynomials with two factors

Multiplying polynomials with three factors

Inequalities Including Graphs

Inequalities worksheets including writing the inequality that matches a graph and graphing inequalities on a number line.

Writing the inequality that matches the graph

Graphing inequalities on number lines

Solving linear inequalities

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LearnAboutMath

Two step equations worksheet: Free worksheet for grade 6

• Author: Noreen Niazi
• Last Updated at: November 14, 2023

Two step equations worksheet

Are you grappling with two-step equations? Fear not! Our specially crafted Two-Step Equations Worksheet is here to guide you through the intricacies of solving these mathematical puzzles.

Unlock the Power of Two-Step Equations:

Step-by-Step Guidance: Our worksheet provides a detailed breakdown of solving two-step equations, making it easy for learners at all levels to follow along.

Abundant Practice Problems: Reinforce your understanding with a plethora of practice problems, carefully curated to cover a spectrum of difficulty levels. From beginner to advanced, we’ve got you covered.

Visual Learning Aids: Grasp the concepts effortlessly with visual aids that simplify the complexities of two-step equations, making learning both effective and enjoyable.

Answer Key for Quick Checks: Verify your solutions promptly with our handy answer key. Immediate feedback accelerates the learning process, helping you identify and rectify any misconceptions.

Perfect for Self-Study or Classroom Use: Whether you’re a student looking to sharpen your skills independently or an educator seeking valuable resources, our Two-Step Equations Worksheet caters to all learning environments.

Empower yourself with the tools you need to conquer two-step equations. Download our worksheet now and embark on a journey of mathematical mastery!

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• https://learnaboutmath.com/power-of-2-math-puzzle-for-kids/

Two-step Equations (Worksheet Bundle)

Subject: Mathematics

Age range: 14-16

Resource type: Lesson (complete)

Last updated

17 January 2019

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srosenfeld11

good, thinly sliced problem set

Empty reply does not make any sense for the end user

Well done; WELL done! THANK you!

Thanks for sharing!

Thanks very much for sharing :)

silvesterjbeaulieu

Fantastic resource - my Year 11 Foundation group LOVE these worksheets!

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Solving Two Step Equations - Christmas Activity - Riddle Worksheet - No Prep!

Description

Solving Two Step Equations Christmas Riddle Activity

worksheet is a fun Christmas Themed Riddle/Joke Activity Solving 2 Step Equations. Students will solve the 9 equations and then use their answers to find the corresponding letters to solve the riddle/joke. *Answer key included!*

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Do you need more Pre-Algebra Christmas Activities? Check out the links below!

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Questions & Answers

Pre algebra adventures.

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