How to Solve One-Step Equations? (+FREE Worksheet!)
How to solve one-step equations, step by step: the rule in plain language, solved examples worked one line at a time, and practice questions so you can try it yourself before moving on.
Solve One-Step Equations: what to notice and how to work it
What to notice first
Common student mistake
Key formulas and cues
A reliable path
- Simplify each sideDistribute and combine like terms before moving variables.
- Collect variablesUse inverse operations to get variable terms on one side and constants on the other.
- Check in the originalSubstitute the solution into the original equation, the simplified line.
Worked examples
Undo addition
- The variable has 7 added to it.
- Undo addition by subtracting 7 from both sides.
- Check: 12 + 7 = 19.
Undo multiplication
- The variable is multiplied by 5.
- Undo multiplication by dividing both sides by 5.
- Check: 5 times 7 is 35.
Try one before moving on
Solve One-Step Equations: pop-up practice
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 ✔})
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 ✔})
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 ✔})
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 ✔})
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 ✔}).
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