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

1. Identify what operation is being applied to the variable.
2. Apply the inverse (opposite) operation to both sides.
3. Simplify to isolate the variable.
4. 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.

1. \(\color{blue}{x + 9 = 17}\)
2. \(\color{blue}{x – 6 = 3}\)
3. \(\color{blue}{4x = 28}\)
4. \(\color{blue}{\frac{x}{3} = 8}\)
5. \(\color{blue}{x + (-5) = 12}\)
6. \(\color{blue}{7x = -35}\)

Answers

1. \(\color{blue}{x = 8}\)
2. \(\color{blue}{x = 9}\)
3. \(\color{blue}{x = 7}\)
4. \(\color{blue}{x = 24}\)
5. \(\color{blue}{x = 17}\)
6. \(\color{blue}{x = -5}\)

The Ultimate Algebra Bundle 2026 From Pre-Algebra to Algebra II

Download

$109.99 Original price was: $109.99.$54.99Current price is: $54.99.

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 is a one-step equation in algebra?

A one-step equation is an equation you can solve with a single inverse operation. The variable has just one thing done to it, such as adding, subtracting, multiplying or dividing by a number. For example, x − 6 = 10 is solved by adding 6 to both sides, giving x = 16. These are the building blocks for two-step and multi-step equations.

How do you solve one-step equations?

Find the operation acting on the variable and undo it on both sides with the opposite operation. Addition undoes subtraction, and multiplication undoes division. For x + 9 = 23, subtract 9 from both sides to get x = 14. For y/4 = 5, multiply both sides by 4 to get y = 20. Then plug your answer back in to check.

How do you solve one-step equations with multiplication and division?

If the variable is multiplied by a number, divide both sides by that number; if it is divided, multiply. For 6x = 42, divide by 6 to get x = 7. For n/3 = 8, multiply by 3 to get n = 24. Watch the signs: −4x = 20 means you divide by −4, so x = −5.

How do you solve one-step equations with fractions?

When the variable is multiplied by a fraction, multiply both sides by its reciprocal. For (2/3)x = 10, multiply by 3/2 to get x = 15. When a fraction is added, subtract it: x + 1/4 = 3/4 gives x = 2/4, which simplifies to 1/2. Simplify your final answer and check it in the original equation.

How do you solve one-step equations with integers?

Use the same inverse operations, but follow the integer sign rules carefully. For x + 8 = −3, subtract 8 from both sides: −3 − 8 = −11, so x = −11. For −5x = −35, divide both sides by −5; a negative divided by a negative is positive, so x = 7. A quick check catches most sign mistakes.

Is it possible to have a one-step equation with no solution?

For a true one-step equation like x + 5 = 2 or 3x = 12, there is always exactly one solution. A no-solution case only shows up when the variable cancels out and leaves a false statement, such as x + 2 = x + 7, which simplifies to 2 = 7. That equation takes more than one step to analyze, so it is not really a one-step equation.

Related Topics

• Multi-Step Equations
• Simplifying Variable Expressions
• Evaluating One Variable
• Evaluating Two Variables
• Order of Operations