Free Interactive Pre-Algebra Tool

One-Step Equations

Use inverse operations to isolate the variable, keep both sides balanced, and verify the solution by substitution.

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Need Help Solving Equations?

Learn Why Inverse Operations Work

Review equality, inverse operations, balancing both sides, isolating the variable, and checking a solution.

Read the One-Step Equations Guide

How It Works

Undo One Operation and Keep the Equation Balanced

A one-step equation has one operation attached to the variable. Use the opposite operation on both sides to isolate the variable.

1

Find the Operation

Decide whether the variable is being added, subtracted, multiplied, or divided.

2

Choose the Inverse

Use the opposite operation to undo what is attached to the variable.

3

Balance Both Sides

Apply the same operation to both sides of the equation.

4

Check the Solution

Substitute the answer into the original equation and confirm both sides match.

Interactive Practice

Solve and Check Each Equation

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Problems 0
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Solve the Equation

Medium

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

x + 6 = 14
The variable has 6 added to it, so undo addition.
  1. 1 Inverse
  2. 2 Balance
  3. 3 Solve
  4. 4 Check
1

Plan the Solution

Which Inverse Operation Is Needed?

Current Step

Current Equation

Medium

Choose the inverse operation.

x + 6 = 14
Undo the operation attached to the variable.

Choose the operation that will isolate the variable.

2

Keep Equality True

Apply the Operation to Both Sides

Locked

Current Equation

Medium

Apply the same operation to both sides.

x + 6 = 14
Both sides must remain equal.

Enter the number used with the inverse operation on both sides.

x + 6 −
=
14 −
3

Isolate the Variable

Enter the Solution

Locked

Current Equation

Medium

Simplify both sides and solve.

x + 6 = 14
The inverse operation leaves the variable alone.
x =
4

Verify the Answer

Does the Solution Make the Equation True?

Locked

Current Equation

Medium

Substitute the solution into the original equation.

x + 6 = 14
Both sides should have the same value.

Compare the left and right sides after substitution.

Keep This Nearby

One-Step Equation Reference

Use the inverse operation on both sides.

Addition Equation Undo addition with subtraction x + 6 = 14 → subtract 6
Subtraction Equation Undo subtraction with addition x − 5 = 9 → add 5
Multiplication Equation Undo multiplication with division 4x = 20 → divide by 4
Division Equation Undo division with multiplication x ÷ 3 = 7 → multiply by 3
Balance Rule Do the same thing to both sides x + 6 − 6 = 14 − 6
Solution Check Substitute into the original equation x = 8 → 8 + 6 = 14

Key Reminders

Avoid the Most Common Equation Mistakes

Check these details before submitting a solution.

Use the Opposite Operation

Addition and subtraction undo each other. Multiplication and division undo each other.

x + 7 = 12 → subtract 7

Do It to Both Sides

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

x − 4 + 4 = 9 + 4

Watch Negative Signs

Adding a negative is not the same as subtracting a positive unless the signs are handled correctly.

x + (−3) = 5 → add 3

Always Check

Substitute the solution into the original equation, not just the simplified equation.

x = 8 → 8 + 6 = 14

Keep Learning

Understand Why Equation Balancing Works

Review inverse operations, equality, balance, negative values, fractions, and complete worked examples in the companion guide.

Read the One-Step Equations Guide