Free Pre-Algebra Guide

One-Step Equations

Learn how to isolate a variable with one inverse operation, keep both sides balanced, and check whether the solution makes the original equation true.

Practice One-Step Equations Read the Guide

A one-step equation can be solved by undoing one operation. The goal is to leave the variable by itself while preserving the equality of the two sides. Whatever operation you apply to one side must also be applied to the other.

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Understand the Equal Sign

What Is an Equation?

An equation states that two mathematical expressions have the same value. The equal sign separates the left side from the right side.

x + 6 = 14
x is the variable.
It represents the unknown value.
x + 6 is the left side.
The variable has 6 added to it.
14 is the right side.
Both sides must have the same value.

The Equal Sign Means “Has the Same Value As”

It does not mean “the answer comes next.” It means the expression on the left and the expression on the right are equal.

Undo the Operation

Inverse Operations

Inverse operations undo each other. To isolate the variable, identify the operation attached to it and apply the opposite operation.

Addition and Subtraction

Opposite Operations

Subtraction undoes addition, and addition undoes subtraction.

Multiplication and Division

Opposite Operations

Division undoes multiplication, and multiplication undoes division.

Equation Operation on Variable Inverse Operation
x + 6 = 14Add 6Subtract 6
x − 5 = 9Subtract 5Add 5
4x = 20Multiply by 4Divide by 4
x/3 = 7Divide by 3Multiply by 3

Preserve Equality

The Balance Rule

An equation remains true when the same operation is applied to both sides.

Example: Solve x + 6 = 14

x + 6 − 6 = 14 − 6

Subtracting 6 from the left cancels the added 6. To keep the equation balanced, subtract 6 from the right as well.

x = 8

Never Change Only One Side

Whatever operation you apply to one side must also be applied to the other.

Undo Addition

Solving Addition Equations

When a number is added to the variable, subtract that number from both sides.

Equation
x + 7 = 19
Inverse operation
Subtract 7 from both sides.
Balanced equation
x + 7 − 7 = 19 − 7
Solution
x = 12

Undo Subtraction

Solving Subtraction Equations

When a number is subtracted from the variable, add that number to both sides.

Example: Solve n − 8 = 5

n − 8 + 8 = 5 + 8
n = 13

Undo Multiplication

Solving Multiplication Equations

A coefficient is a number multiplying the variable. Divide both sides by that coefficient.

Example: Solve 4x = 28

4x ÷ 4 = 28 ÷ 4
x = 7

Undo Division

Solving Division Equations

When the variable is divided by a number, multiply both sides by that number.

Example: Solve x 5 = 6

5 · x 5 = 5(6)

The factor of 5 cancels the denominator of 5.

x = 30

Track Every Sign

One-Step Equations With Negative Numbers

The same inverse-operation rules apply when constants, coefficients, or solutions are negative.

Negative Solution

x + 9 = 4

x = 4 − 9 = −5
Negative Coefficient

−3x = 18

x = 18 ÷ (−3) = −6

Work With Rational Values

One-Step Equations With Fractions

Fraction equations follow the same balance rule. Multiply by the denominator to undo division.

Example: Solve x 10 = − 4 5

  1. Multiply both sides by 10.
  2. The denominator of 10 cancels on the left.
  3. Compute 10 × (−4/5).
x = 10 · − 4 5 = −8
x = −8

Verify the Result

How to Check a Solution

Substitute the proposed solution into the original equation. If both sides have the same value, the solution is correct.

Check x = 8 in x + 6 = 14

8 + 6 = 14
14 = 14, so x = 8 is correct.

Apply the Rules

Worked One-Step Equation Examples

Addition

Solve x + 12 = 20

  1. Subtract 12 from both sides.
  2. x + 12 − 12 = 20 − 12.
  3. x = 8.
Subtraction

Solve n − 7 = −3

  1. Add 7 to both sides.
  2. n − 7 + 7 = −3 + 7.
  3. n = 4.
Multiplication

Solve −5y = 35

  1. Divide both sides by −5.
  2. −5y ÷ (−5) = 35 ÷ (−5).
  3. y = −7.
Division

Solve m 4 = −6

  1. Multiply both sides by 4.
  2. The denominator cancels.
  3. m = −24.
Negative Constant

Solve p + (−8) = 3

  1. Adding −8 is the same as subtracting 8.
  2. Add 8 to both sides.
  3. p = 11.
Fraction Result

Solve 6a = 5

  1. Divide both sides by 6.
  2. The coefficient cancels.
  3. a = 5 6 .

Watch for These Errors

Common Mistakes With One-Step Equations

Using the Same Operation Instead of the Inverse

If 6 is added to x, subtract 6.

Changing Only One Side

Apply the same operation to both sides.

Ignoring a Negative Coefficient

In −4x = 20, divide by −4, not 4.

Misreading a Fraction Bar

A fraction bar represents division.

Stopping Before the Variable Is Isolated

The final equation should look like x = number.

Skipping the Check

Substitution catches sign and arithmetic errors.

A Reliable Process

Steps for Solving One-Step Equations

1. Identify the variable
Find the letter you need to isolate.
2. Identify the operation
Determine what is being done to the variable.
3. Choose the inverse
Use the operation that undoes the original operation.
4. Apply it to both sides
Keep the equation balanced.
5. Simplify
Write the variable alone with its solution.
6. Check
Substitute into the original equation.

Practice Solving One-Step Equations

Choose the inverse operation, apply it to both sides, solve for the variable, and verify your result.

Open the One-Step Equations Tool

Continue Learning

Related Math Resources

Interactive One-Step Equations Practice

Solve addition, subtraction, multiplication, and division equations with guided feedback.

Evaluating Algebraic Expressions

Review variables and substitution before checking equation solutions.

Order of Operations Guide

Review the arithmetic used when simplifying equations.

Integer Addition Practice

Strengthen positive and negative number skills.

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