How to Solve One-Step Equations? (+FREE Worksheet!)
One-step equations are the simplest equations in algebra — they require only a single operation to isolate the variable. Mastering them builds the logical foundation for solving every other type of equation in Algebra 1 and beyond. The key idea is to use the inverse operation to undo what is being done to the variable.
What Is a One-Step Equation?
A one-step equation is an equation that can be solved by performing exactly one operation on both sides. Examples include \(\color{blue}{x + 7 = 15}\), \(\color{blue}{x – 4 = 9}\), \(\color{blue}{3x = 21}\), and \(\color{blue}{\frac{x}{5} = 6}\). In each case, one operation separates the variable from the solution.
The Four Types of One-Step Equations
Addition equations — subtract from both sides
If a number is added to the variable, subtract that number from both sides.
- \(\color{blue}{x + 7 = 15 \rightarrow x = 15 – 7 = 8}\)
Subtraction equations — add to both sides
If a number is subtracted from the variable, add that number to both sides.
- \(\color{blue}{x – 4 = 9 \rightarrow x = 9 + 4 = 13}\)
Multiplication equations — divide both sides
If the variable is multiplied by a number, divide both sides by that number.
- \(\color{blue}{3x = 21 \rightarrow x = 21 \div 3 = 7}\)
Division equations — multiply both sides
If the variable is divided by a number, multiply both sides by that number.
- \(\color{blue}{\frac{x}{5} = 6 \rightarrow x = 6 \times 5 = 30}\)
Step-by-Step Summary
- Identify what operation is being applied to the variable.
- Apply the inverse (opposite) operation to both sides.
- Simplify to isolate the variable.
- Check: substitute your answer back into the original equation to verify it is correct.
Watch: Solving One-Step Equations (Video Lesson)
Math Antics explains solving basic one-step equations with addition and subtraction — visually and clearly:
One-Step Equations – Worked Examples
Example 1: Solve \(\color{blue}{x + 7 = 15}\).
Subtract 7 from both sides: \(\color{blue}{x = 15 – 7 = 8}\).
Check: \(\color{blue}{8 + 7 = 15 &\#x2714;}\)
Answer: \(\color{blue}{x = 8}\)
Example 2: Solve \(\color{blue}{x – 4 = 9}\).
Add 4 to both sides: \(\color{blue}{x = 9 + 4 = 13}\).
Check: \(\color{blue}{13 – 4 = 9 &\#x2714;}\)
Answer: \(\color{blue}{x = 13}\)
Example 3: Solve \(\color{blue}{3x = 21}\).
Divide both sides by 3: \(\color{blue}{x = 21 \div 3 = 7}\).
Check: \(\color{blue}{3(7) = 21 &\#x2714;}\)
Answer: \(\color{blue}{x = 7}\)
Example 4: Solve \(\color{blue}{\frac{x}{5} = 6}\).
Multiply both sides by 5: \(\color{blue}{x = 6 \times 5 = 30}\).
Check: \(\color{blue}{\frac{30}{5} = 6 &\#x2714;}\)
Answer: \(\color{blue}{x = 30}\)
More Practice: One-Step Equations Video
Khan Academy walks through solving one-step equations with addition and subtraction, showing each step:
Exercises for One-Step Equations
Solve for the variable.
- \(\color{blue}{x + 9 = 17}\)
- \(\color{blue}{x – 6 = 3}\)
- \(\color{blue}{4x = 28}\)
- \(\color{blue}{\frac{x}{3} = 8}\)
- \(\color{blue}{x + (-5) = 12}\)
- \(\color{blue}{7x = -35}\)
Answers
- \(\color{blue}{x = 8}\)
- \(\color{blue}{x = 9}\)
- \(\color{blue}{x = 7}\)
- \(\color{blue}{x = 24}\)
- \(\color{blue}{x = 17}\)
- \(\color{blue}{x = -5}\)
Free One-Step Equations Worksheet
Ready to practice on your own? Download our free One-Step Equations worksheet below, work through each problem at your own pace, and then check your answers. If a few give you trouble, scroll back up to the worked examples and try again — steady practice is the surest way to master One-Step Equations before a quiz or test.
Download Solving One Step Equations Worksheet
Frequently Asked Questions
What does “inverse operation” mean?
The inverse (opposite) operation undoes another operation. Addition and subtraction are inverses; multiplication and division are inverses. To isolate a variable, apply the inverse operation to both sides of the equation.
Why do I have to do the same thing to both sides?
An equation is like a balanced scale. Whatever you do to one side, you must do to the other to keep the balance. That is the foundation of all equation solving.
How do I check my answer?
Substitute your answer back into the original equation and evaluate both sides. If they are equal, your solution is correct. For example, for \(\color{blue}{x = 8}\) in \(\color{blue}{x + 7 = 15}\): \(\color{blue}{8 + 7 = 15 &\#x2714;}\).
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