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.

Want to see why this works? In our free algebra balance scale game, you solve one-step equations like x + 3 = 7 by taking the same number of weights off both pans, and the written equation updates after every move.

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 ✔})
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.

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})

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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