How to Solve Two-Step Equations
Unlock the secrets to solving for X with our how-to guide.
Published:
Feb 2025
Key takeaways
- • Don’t make it too complicated – While two-step equations might look a little scary because of the different parts, they’re really not that bad.
- • Identify the different parts of the equation – You’ll need to look for the variable, the large integer, and the small integer.
- • It really only takes two steps – If you’ve gone past step two, you’ve gone too far. Keep it simple!
Table of contents
The older you get, the more complex your math classes become. One of the basic skills you will need as you progress through middle and high school? How to solve two-step equations.
When you first look at an algebraic equation, you may be tempted to run away. Don’t worry—it’s not nearly as complicated as it looks. Today, we’ll explore how to approach two-step equations so that you can impress your math teacher and crush your next math test.
Definition of Two-Step Equations
A two-step equation is exactly what it sounds like: an equation that can be solved in two steps. Typically, a two-step equation consists of a single variable, such as X or Y, and two integers. Each equation has two sides, a left side and a right side. The variable and one integer will usually be on the left side of the equal sign, and the other integer will be on the right side of the equal sign, or the right side of the equation.
Importance of Solving Two-Step Equations
Learning how to solve a two-step equation is an important step on your mathematics journey. Later, you’ll need to solve equations with two variables. You will also need to learn the order of operations so that you’re able to simplify more complex equations. Learning to solve two-step equations is an important stepping stone into complicated math such as precalculus, calculus, and beyond!
Understanding the Basics
Before we dive into solving two-step equations, there are a few terms you need to understand. Let’s review the basics of equations so we’re all speaking the same language.
An equation is a mathematical statement typically separated by an equals sign (=) that indicates the equality of two mathematical expressions. They are crucial in mathematics and science, helping us solve problems, describe relationships, and model real-world phenomena. They can range from simple linear equations like 3𝑥 + 6 = 36, also known as a two-step equation, to complex systems involving multiple variables and higher-order terms.
Components of Two-Step Equations
You will need to understand a few terms in order to talk about and solve a two-step equation. Let’s take a look at the example from above, 3X+6 = 36.
- The variable – The variable is typically what you’re looking for in an equation. In this case, X is the variable.
- The coefficient – A coefficient is the number preceding a variable that multiplies that variable. In our example equation, 3 is the coefficient.
- Integers – “Integer” is just another term for “number.” Usually, in two-step equations, you will have a larger integer and a smaller integer. In our example equation, 36 is the larger integer and 6 is the smaller integer.
If you remember your multiplication tables, you’ll know that the coefficient and the variable are both factors that, when multiplied together, give you a particular number, so to solve for X, you will need to divide by the coefficient.
Steps to Solve Two-Step Equations
So, how do you approach a two-step equation? You’ll need your addition, subtraction, multiplication, and division skills to be successful. Let’s take a closer look.
Step 1: Isolate the Variable by Either Adding or Subtracting the Smaller Integer from the Larger Integer
In this equation, you will need to subtract 6 from 36. Once you complete this step, the equation should look like:
3X + 6 = 36
-6 -6
3X = 30
Step 2: Simplify by Dividing the Integer by the Coefficient
Now that you’ve isolated the variable, you’ll divide the remaining integer by the coefficient. Once you complete this step, the equation should look like:
3X = 30
Then, divide the integer by the coefficient to solve for X.
30/3 = 10
X = 10
Check Your Solution
Now, to make sure you are correct, you can check your solution by plugging the variable into the original equation.
3X + 6 = 36
3(10) = 30
30+ 6 = 36
Congratulations! You’ve successfully solved a two-step equation!
Practice Problems
Here are some two-step equation problems for you to practice:
Problem 1: Solve for z
2z − 7 = 13
Problem 2: Solve for a
5a + 10 = −20
Problem 3: Solve for b
3b/2 + 4 = 10
Some Other Things to Consider
While solving two-step equations is simple, there are a few important things to remember in order to be successful.
Make sure you always follow your order of operations. You don’t want to divide X by the coefficient before you’ve subtracted the smaller integer from the larger integer. Otherwise, you’re going to get some incorrect answers. You also want to make sure you’ve mastered addition, subtraction, division, and multiplication prior to starting in on any two-step equations.
Do That Two-Step!
While completing a two-step equation may seem daunting at first, it’s really as easy as two steps! As long as you remember the order of operations and how to add, subtract, divide, and multiply, you’ll be finding variables in absolutely no time.
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FAQs about Two Step Equations
This will largely depend on the equation itself. Typically, you’ll want to use division last when you’re trying to isolate a variable from its coefficient. Once you subtract the smaller integer (or number) from the larger integer, you should have the variable and its coefficient on the left side of the equation and a number on the right. Then, divide that number by the coefficient to solve for your variable.
Not always! Variables can be any number of letters. You may be asked to solve for Y or maybe even for N! However, X is the most common variable in a two-step equation.
The order of operations is the order you use to work out mathematical expressions. You can use the acronym PEMDAS to remember the order of operations easily, or Please Excuse My Dear Aunt Sally. PEMDAS stands for: parentheses, exponents, multiplication, division, addition, and subtraction. Always start with parentheses and end with subtraction!
First, you will need to isolate the variable that you are solving for, probably by using subtraction or addition to get the variable alone. Then, divide by the coefficient to solve for the variable (x, y, n, or any other variable that may show up in your equation!)
