Solving two-step equations is one of the most important skills that you need to master in studies of algebra. This is truly a skill that comes up over and over again throughout studies of mathematics. And that’s why I’ve put together this collection of solving 2 step equations worksheets for you!
These free printable worksheets will help you practice solving for the value of the unknown variables in linear equations. Practicing multi-step equations is important to help you develop foundational skills that will be built upon in further studies of mathematics.
Throughout my career as a math teacher I have seen many students struggle with much more advanced equation solving as a result of missing foundations. Completing additional practice by using practice worksheets like those found below will help you avoid encountering further struggles down the road!
Let’s dig into this two step equations worksheet collection!
Two-step equations contain a combination of algebraic expressions that form math sentences. These types of equations require you to perform two steps in order to determine the value of the unknown variables.
If this is your first time solving a 2-step equation, don’t worry! Two-step equations are solved using a similar process to solving one-step equations. However, there is the obvious addition of an extra step.
A 2-step equation problem will require you to apply two operations in order to determine the value of the variable that is unknown. You will be given two sides of the equation, an unknown variable, and a series of operations.
The first step is to identify the side of the equation that has the unknown variable on it. In simple terms, this will be whichever side has the “letter” on it. Your main goal will be to isolate this unknown variable.
The second step is to “undo” whatever the operations are that are keeping the variable from being isolated. To do this, we apply inverse operations. This is just a fancy way of saying “do the opposite of whichever operations are there”. Typically this involves completing order of operations in reverse.
After you have performed each step, you will be able to identify the value of the variable!
In order to help you get ready for the math worksheets linked below, I wanted to share an example of a two-step equation. Consider the following 2-step equation:
As you can see, this equation has an unknown variable on the left hand side of the equation that is multiplied by 3 before being subtracted by 4. Because of this, unlike one-step equations, this equation cannot be solved in a single step.
To begin, we apply an inverse operation to “undo” the subtraction by 4. This inverse operation is addition by 4. We do this on both sides of the equation to ensure that we do not unbalance the equation:
We now have a single step equation! Since the variable is multiplied by 3, the inverse operation will be to divide both sides by 3. This results in:
We have now successfully solved this 2-step equation for the value of the unknown variable!
Remember that you can always check your answer by taking the value of the variable and placing it back into the original equation. If the left hand side of the equation is equal to the right hand side, you have solved the equation correctly!
For example, replacing p with \(p = 4\) results in:
So we can confirm that the equation was solved correctly! Checking your answer is a fun activity that can give you a boost of confidence if this is your first time solving a 2-step equation!
Now that you have completed some additional practice using the example above, it’s time to dig into these solving 2 step equations worksheets! I have included a wide variety of problem types across three worksheets to help you develop a deep understanding of the equation solving process.
The two step equations worksheet linked below is an excellent resource if this is your first time solving algebraic equations. Positive and negative integers are familiar to most mathematics students, so it makes sense to try solving these linear equations first!
After solving each equation, be sure to check the answer key to verify that you fully understand the process for solving two-step equations involving positive integers and negative integers.
After you have had some time to practice with equations involving integers, move forward with decimals and fractions to deepen your understanding!
Download the PDF worksheet by clicking below!
After you have spent some time familiarizing yourself with 2-step equations involving negative and positive integers, take a look at the following practice worksheets. Next up is a PDF worksheet that focuses on solving equations involving decimals.
You will see that the equations found in this PDF worksheet include decimal coefficients. The process that you use to solve these 2-step equations is exactly the same as the steps you completed previously.
I have included a wide variety of types of decimal answers throughout these problems. You will see examples of terminating decimals as well as non-terminating decimals!
Be sure to review the answer key after you complete each problem and take note of each type of decimal number!
Download the PDF worksheet by clicking below!
The last of the practice worksheets that I have included focuses on solving equations involving fractions. These types of equations are the most challenging of this set. Fractions are something that many students find intimidating. However, the process to solve a two-step equation that contains fractions is the same!
After you complete this worksheet, check the answer key to make sure you fully understand how to solve 2-step equations involving fractions!
Download the PDF worksheet by clicking below!
Equation solving is one of the most important skills that you can develop as a student who is studying mathematics. Whether you are learning to use algebra to solve real-world word problems or a tricky test question, understanding how to solve 2-step equations is your first step toward developing a strong foundation of basic algebra skills.
And it is important to remember that you will need strong algebra skills as you move forward to start solving much more complex problems such as quadratic equations, linear inequalities, and exponential equations.
I hope you found these practice worksheets to be useful additional practice problems as you work to deepen your understanding of two-step equation solving!
If you are looking to apply your understanding of linear equations to word problems, check out this linear equations word problems worksheet!
Did you find this breakdown of two-step equations helpful? Share this post with a friend and subscribe to Math By The Pixel on YouTube for more helpful mathematics content!
