Multi Step Equations Worksheet Library

Free Solving Multi Step Equations Worksheets and Answer Keys

Download Free PDF Multi-Step Equations Worksheets and Answer Keys

Welcome to the Mashup Math Multi Step Equations Worksheet Library, where you can download free PDF worksheets with a variety of practice problems.

Each solving multi step equations worksheet in the library below is available as a PDF file that is easy to download or print. Each practice worksheet includes a variety of practice problems and a complete answer key.

You can click on any of the blue text links below to preview, download, or print any of our free worksheets. The second section of this page features a short review of how to solve a variety of multi-step equations, similar to the practice problems on our solving multi step equations worksheets pdf library.

Each PDF worksheet shared in the library below is a sample from the Mashup Math Practice Worksheet Libraries available on our website, where you can access tons of free algebra practice worksheets. | Reference Guide: How to Download/Print

Multi Step Equations Worksheet Library

Two-Sided Equations

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Extended Practice (Beginner)

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Extended Practice (Intermediate)

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Multi Step Equations Worksheet Review

Are you struggling to solve any of the practice problems on any multi step equations worksheet shared in our free library? If so, this section will give you a step-by-step review of how to solve many types of problems that you will see on our solving multi step equations worksheets pdf downloads.

When it comes to solving multi step algebraic equations, the number one goal is always to isolate the variable by itself on one side of the equation by using inverse operations to rearrange the equation.

Inverse operations refers to the fact that each of the four main math operations—addition, subtraction, multiplication, and division—has an inverse, or opposite operation. The inverse of addition is subtraction and the inverse of subtraction is addition. And, the inverse of multiplication is division and the inverse of division is multiplication. With this in mind, let’s work through some practice problem examples of how to solve a mult-step algebraic equation.

Solving Multi-Step Equations Example #1

Example: Solve for x: 3x + 4 = 13

Let’s start off with a very simple multi-step equation, where we have to solve for x.

As with solving any algebraic equation, the aim is to isolate the variable (which is x in this case). We can do that using inverse operations to rearrange the equation, 3x + 4 = 13, so that x is by itself on one side of the equals sign, as follows:

  • Step #1: Isolate the x-term

  • 3x + 4 = 13

  • 3x + 4 -4 = 13 -4

  • 3x = 9

Completing step one required us to isolate the x term by moving the +4 to the right side of the equation by applying inverse operations (the opposite of adding 4 is subtracting 4). After completing the first step, we are left with a new simplified equation, 3x=9, that we can solve as follows:

  • Step #2: Solve for x

  • 3x = 9

  • (3x)/3 = 9/3

  • x = 3

For the second step, we had to divide both sides of the equation by 3 to get x by itself, resulting in x=3.

Final Answer: x=3 is the solution to the two-step equation 3x + 4 = 13.

We can do a check to confirm that our answer is correct by taking x=3 and substituting it into the equation that we started with (3x+4=13 in this case) and seeing if the left-side of the equation and the right-side of the equation equal the same value. If they do, then you know that you have solved the problem correctly. If not, then it is likely the case that you made an error somewhere along the process of solving the equation, and you should go by and solve the problem again.

Example #1 Check:

  • 3x + 4 = 13

  • 3(3) +4 = 13

  • 9 + 4 = 13

  • 13 = 13 ✔

Since x=3 work out, we have successfully solved this algebraic equation! Figure 01 below illustrates how we solved Example #1 in two steps.

 

Figure 01: Multi Step Equations Worksheet Review: Example #1 Solved

 

Solving Two-Step Equations Example #2

Example: Solve for x: 7𝑥 + 9 = 4𝑥 + 24

For our second example, notice that there is an x-term on each side of the equals sign. Our goal, however, is isolate the x, and we can do that by first isolating the x-term as follows:

  • Step #1: Isolate the x-term part one

  • 7𝑥 + 9 = 4𝑥 + 24

  • 7x -4x + 9 = 4x -4x + 24

  • 3x + 9 = 24

Now we have a new simplified equation, 3x +9 =24. Our next step is to completely isolate the x-term as follows:

  • Step #2: Isolate the x-term part two

  • 3x + 9 = 24

  • 3x + 9 -9 = 24 -9

  • 3x = 15

Now we are left with 3x=15. The last step to solving this multi step equation is to get x by itself on the left-side of the equation. Since 3x means “3 times x,” we can use inverse operations (i.e. division is the inverse of multiplication) as follows:

  • 3x = 15

  • (3x)/3 = 15/3

  • x = 5

Final Answer: x=5 is the solution to the multi-step equation 7𝑥 + 9 = 4𝑥 + 24

We can check our answer by taking x=5 and substituting them back into 7𝑥 + 9 = 4𝑥 + 24 as follows:

  • 7𝑥 + 9 = 4𝑥 + 24

  • 7(5) + 9 = 4(5) + 24

  • 35 + 9 = 20 + 24

  • 44 = 44 ✔

Since we ended up with 44 on each side of the equals sign, we can say that our answer checks out and this multi step equation has been successfully solved.

The image in Figure 02 shows the step-by-step process for solving this multi-step equation below.

 

Figure 02: Multi Step Equations Worksheet Review: Example #2 Solved