Solving Equations · Distribute & combine · 5.1

Distribute first.

When there are brackets, distribute first to clear them, then solve the two-step equation. 3(x − 2) = 9 → 3x − 6 = 9 → 3x = 15 → x = 5.

01 / THE IDEA

See it work.

Watch the method

Distribute first

3(x − 2) = 9 → 3x − 6 = 9 → x = 5.

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3(x−2)=93(x - 2) = 9
1

The equation

Solve for x — find the value that makes both sides equal.

3(x−2)=93(x - 2) = 9
2

Simplify each side

Distribute and combine like terms on each side.

3x−6=93x - 6 = 9
3

Move the constant

Add 6 to both sides.

3x=153x = 15
4

Divide by the coefficient

Divide both sides by 3 to get x by itself.

x=5x = 5
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Solve for x.

Type the value of x — a number or a fraction like 3/2.

streak 0
best 0
…x =
— / WHY IT WORKS

The idea underneath.

Clear the brackets

Multiply every term inside the brackets by the number outside, then solve normally.

Why it works

3(x − 2) = 3x − 6.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Solve 2(x - 5) = 4

1

The equation

Solve for x — find the value that makes both sides equal. 2(x - 5) = 4

2

Simplify each side

Distribute and combine like terms on each side. 2x - 10 = 4

3

Move the constant

Add 10 to both sides. 2x = 14

4

Divide by the coefficient

Divide both sides by 2 to get x by itself. x = 7

EX 2medium

Solve 2(x + 5) = 20

1

The equation

Solve for x — find the value that makes both sides equal. 2(x + 5) = 20

2

Simplify each side

Distribute and combine like terms on each side. 2x + 10 = 20

3

Move the constant

Subtract 10 from both sides. 2x = 10

4

Divide by the coefficient

Divide both sides by 2 to get x by itself. x = 5

EX 3hard

Solve 5(x + 5) = 40

1

The equation

Solve for x — find the value that makes both sides equal. 5(x + 5) = 40

2

Simplify each side

Distribute and combine like terms on each side. 5x + 25 = 40

3

Move the constant

Subtract 25 from both sides. 5x = 15

4

Divide by the coefficient

Divide both sides by 5 to get x by itself. x = 3

04 / COMMON TRAPS

Where students slip.

Trap

Multiplying only the first term.

Fix

Distribute to EVERY term in the brackets.

Trap

Forgetting the sign inside.

Fix

3(x − 2) = 3x − 6, not 3x − 2.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Solve 2(x - 6) = -2

Need a hint?
  • Distribute across the brackets.
  • Then solve the two-step.
C2

Solve 2(x - 6) = -16

Need a hint?
  • Distribute across the brackets.
  • Then solve the two-step.
C3

Solve 2(x + 2) = 18

Need a hint?
  • Distribute across the brackets.
  • Then solve the two-step.
C4

Solve 2(x + 4) = 20

Need a hint?
  • Distribute across the brackets.
  • Then solve the two-step.
Apply

Apply (4)

A1

Solve 2(x - 1) = 12

Need a hint?
  • Distribute across the brackets.
  • Then solve the two-step.
A2

Solve 4(x - 4) = 12

Need a hint?
  • Distribute across the brackets.
  • Then solve the two-step.
A3

Solve 3(x - 3) = 9

Need a hint?
  • Distribute across the brackets.
  • Then solve the two-step.
A4

Solve 5(x - 4) = -40

Need a hint?
  • Distribute across the brackets.
  • Then solve the two-step.
Extension

Extension (4)

E1

Solve 4(x + 4) = 32

Need a hint?
  • Distribute across the brackets.
  • Then solve the two-step.
E2

Solve 4(x - 3) = 12

Need a hint?
  • Distribute across the brackets.
  • Then solve the two-step.
E3

Solve 2(x + 1) = 16

Need a hint?
  • Distribute across the brackets.
  • Then solve the two-step.
E4

Solve 3(x + 4) = 0

Need a hint?
  • Distribute across the brackets.
  • Then solve the two-step.