Free Interactive Pre-Algebra Tool

Two-Step Equations

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

Start Practicing Read the Guide

Need Help Solving Equations?

Learn Why Constant Operations Work

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

Read the Two-Step Equations Guide

How It Works

Undo Two Operations in the Correct Order

A two-step equation has two operations attached to the variable. Undo addition or subtraction first, then undo multiplication or division.

1

Find the Outer Operation

Identify the addition or subtraction that must be undone first.

2

Undo the Constant

Add or subtract the same value on both sides.

3

Undo the Coefficient

Divide or multiply both sides to isolate the variable.

4

Check the Solution

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

Interactive Practice

Solution Each Two-Step Equation

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Problems 0
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Solution the Two-Step Equation

Medium

Undo the constant term first, then undo the coefficient.

3x + 5 = 20
First subtract 5 from both sides, then divide both sides by 3.
  1. 1 Constant
  2. 2 Coefficient
  3. 3 Solution
  4. 4 Check
1

Plan the Solution

Which Constant Operation Is Needed?

Current Step

Current Equation

Medium

Choose the inverse operation.

3x + 5 = 20
Undo the operation attached to the variable.

Choose the inverse operation for the constant term.

2

Keep Equality True

Remove the Constant Term

Locked

Current Equation

Medium

Apply the same operation to both sides.

3x + 5 = 20
Both sides must remain equal.

Enter the value used to undo the constant on both sides.

3x + 5 −
=
20 −
3

Undo the Coefficient

Apply the Second Inverse Operation

Locked

Current Equation

Medium

Divide or multiply both sides to leave the variable alone.

3x + 5 = 20
The second inverse operation isolates the variable.

Enter the divisor or multiplier used on both sides.

3x ÷
=
15 ÷
4

Enter and Verify the Solution

What Is the Solution?

Locked

Current Equation

Medium

Enter the solution, then verify it in the original equation.

3x + 5 = 20
The completed solution should make both sides equal.

Enter the value of the variable.

x =

Keep This Nearby

Two-Step Equation Reference

Undo addition or subtraction first, then multiplication or division.

ax + b = c Subtract b first, then divide by a 3x + 5 = 20 → subtract 5 → divide by 3
ax − b = c Add b first, then divide by a 4x − 7 = 13 → add 7 → divide by 4
x/a + b = c Subtract b first, then multiply by a x/3 + 2 = 7 → subtract 2 → multiply by 3
Work Backward Undo the outside operation before the coefficient Addition or subtraction comes off first
Balance Rule Apply every operation to both sides 3x + 5 − 5 = 20 − 5
Solution Check Substitute into the original equation x = 5 → 3(5) + 5 = 20

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 = 20

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 Two-Step Equations Guide