One Step Equations Worksheet Library

Free Solving One Step Equations Worksheets with Answer Keys

Welcome to the Mashup Math One Step Equations Worksheet Library, where you can download free PDF practice worksheets for a variety of topics related to solving one-step algebraic equations.

Each solving one step equations worksheet in the library below can be downloaded as printable PDF file. Each worksheet includes several practice problems along with a complete answer key on the second page.

To download any of our one-step equations worksheets, simply visit the library below and click on any of the text links to open the worksheet’s preview page. From this page, you can download the worksheet as a PDF file and/or print the worksheet with our without the corresponding answer key.

Below the worksheet library, you will find a short review section that recaps solving one step equations. This section includes several practice problems that are worked out and solved step-by-step. If you are your students are struggling with any of the practice problems on our one-step equations worksheets, then we highly recommend visiting this section before moving forward.

All of the one step equations worksheets available below are free sample activities from the Mashup Math Infinite Math Worksheet Libraries for Grades K-12. If you want access to more free topic-specific PDF math worksheets, visit our website to access the full library. | Quick Help: How to Download/Print

One Step Equations Worksheet Library

▶️ Solving one-step algebraic equations (add/subtract) (A)

▶️ Solving one-step algebraic equations (add/subtract) (B)

▶️ Solving one-step algebraic equations (multiply/divide) (A)

▶️ Solving one-step algebraic equations (multiply/divide) (B)

▶️ Solving one-step algebraic equations (4 operations) (A)

▶️ Solving one-step algebraic equations (4 operations) (B)

▶️ Solving one-step algebraic equations (4 operations) (C)

▶️ Extended Practice: Solving One-Step Equations (A)

▶️ Extended Practice: Solving One-Step Equations (B)

▶️ Variables and equations word problems (A)

▶️ Variables and equations word problems (B)

▶️ Variables and equations word problems (C)

▶️ Solving One-Step and Two-Step Equations Word Problems (A)

▶️ Solving One-Step and Two-Step Equations Word Problems (B)

Do You Want More FREE Practice Worksheets and Answers Keys? 🛑

If so, check out the Mashup Math K-12 Infinite Math Worksheets Library, where you will find hundreds of topic-specific math worksheets!

One Step Equations Worksheet Review

Welcome to our solving one-step equations worksheet review! In the event that you or your students are having a hard time solving any of the problems on our solving one step equations worksheets, this quick review will teach you everything you need to know about how to solve a one-step algebraic equation.

Before we get to any practice problems, it is imperative that you understand two things when it comes to solving a one-step algebraic equation":

1. The goal of solving any algebraic equation is to get the variable by itself on one side of the equals sign.

2. You can achieve this goal of isolating the variable by rearranging the equation by using inverse operations.

As long as you understand those two main points, then you can learn how to solve any one-step algebraic equation with relative ease.

Now, let’s dive deeper into point #2. What does it mean when we say that we can isolate the variable by using inverse operations? In math, there are four main operations: addition, subtraction, multiplication, and division, and each operation has an inverse, or opposite.

First, let’s focus on the fact that addition and subtraction are inverses of each other. In other words:

• addition is the inverse of subtraction

• subtraction is the inverse of addition

For example, the inverse of adding 3 to a number is subtracting 3 from the number.

Next, we have multiplication and division, which are, in fact, inverses of each other. In other words:

• multiplication is the inverse of division

• division is the inverse of multiplication

For example, the inverse of multiplying a number by 8 is dividing the number by 8.

Inverse operations can be used to rearrange an equation and to “cancel out” terms, which is incredibly useful since the goal of solving an algebraic equation is to isolate the variable (i.e. get the variable by itself).

Now, let’s take a look at a few examples of how to solve a one-step equation.

Solving One-Step Equations Example #1

Example: Solve for x: x + 8 = 10

For this first example, our goal is to get the variable, x, by itself, and we can use inverse operations to do that.

In this case, we can get x by itself by taking the +8 term and moving it to the right side of the equation. The opposite of +8 is -8, so we just have to subtract 8 from both sides of the equation to isolate x as follows:

• x + 8 = 10

• x + 8 -8 = 10 - 8

• x = 2

Final Answer: x=2 is the solution to the one-step equation x + 8 = 10.

How do we know that our final is correct? Whenever you solve a one step equation, you should always check your answer (x=2 in this case) by substituting it back into the original equation to see if the left and right-sides of the equation equal the same value (which validates that your answer is correct).

• x + 8 = 10

• (2) + 8 = 10

• 10 = 10 ✔

Clearly, our answer has worked out and we can say that x=2 is the answer.

Solving One-Step Equations Example #2

Example: Solve for x: -5 + x = -2

Just like the previous example, our goal is to get x by itself using inverse operations.

In this case, we can to move the -5 term to the right-side of the equation to isolate x as follows:

• -5 + x = -2

• -5 +5 + x = -2 +5

• x = 3

Final Answer: x=3 is the solution to the one-step equation -5 + x = -2.

We can now check our answer by substituting x=3 back into the original equation:

• -5 + x = -2

• -5 + (3) = -2

• -2 = -2 ✔

The step-by-step process for solving Example #2 is shown in Figure 02 below.

Solving One-Step Equations Example #3

Example: Solve for x: 4x = 28

For this third example, which is similar to many of the problems on our one-step equations worksheets, it is important to note that 4x means “4 times x,” and remember that the inverse of multiplication is division. So, we can get by itself by dividing both sides of the equation by 4 as follows:

• 4x = 28

• (4x)/4 = (28)/4

• x = 7

Final Answer: x=7 is the solution to the one-step equation 4x = 28.

Let’s go ahead and check our answer by substituting:

• 4x = 28

• 4(7) = 28

• 28 = 28 ✔

Figure 03 below illustrates how we used inverse operations to solve this one-step algebraic equation.

Solving One-Step Equations Example #4

Example: Solve for x: -12 = x/3

For our fourth and final example, notice that our variable, x, is the numerator of a fraction. The fraction x/3 means “x divided by 3,” and the inverse of division is multiplication. So, we can isolate x simply by multiplying both sides by 3 as follows:

• -12 = x/3

• 3(-12) = 3(x/3)

• -36 = x

• x = -36

Notice that, in this example, our variable, x, ended up being isolated on the right-side of the equation. This is totally fine because -36=x means the same as x=-36, so we can conclude that:

Final Answer: x=-36 is the solution to the one-step equation -12 = x/3.

Finally, let’s make sure that our answer is correct by performing a quick check:

• -12 = x/3

• -12 = (-36)/3

• -12 = -12 ✔

The graphic in Figure 04 shows the step-by-step process for how we used inverse operations to solve this final example.

Now that you have some more experience with solving one-step algebraic equations using inverse operations, go ahead an revisit the one step equations worksheet library above and try some more practice problems. Use the answer key on the second page to assess your progress as you go. The more problems that you work on, the better you will become at solving one-step equations.