Solving Equations · Distribute & combine · 5.4

Multi-step mastery.

The full method: distribute, combine like terms, collect the variable on one side, move the constants, then divide. Take it one clean step at a time.

01 / THE IDEA

See it work.

Watch the method

Multi-step mastery

Distribute → combine → collect → solve.

1 / 4
4(x−1)=84(x - 1) = 8
1

The equation

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

4(x−1)=84(x - 1) = 8
2

Simplify each side

Distribute and combine like terms on each side.

4x−4=84x - 4 = 8
3

Move the constant

Add 4 to both sides.

4x=124x = 12
4

Divide by the coefficient

Divide both sides by 4 to get x by itself.

x=3x = 3
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.

The whole routine

Brackets, then like terms, then variables together, then constants, then divide.

Why it works

Tidy, gather, isolate.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Solve 4(x - 5) = -16

1

The equation

Solve for x — find the value that makes both sides equal. 4(x - 5) = -16

2

Simplify each side

Distribute and combine like terms on each side. 4x - 20 = -16

3

Move the constant

Add 20 to both sides. 4x = 4

4

Divide by the coefficient

Divide both sides by 4 to get x by itself. x = 1

EX 2medium

Solve 3(x + 5) = 27

1

The equation

Solve for x — find the value that makes both sides equal. 3(x + 5) = 27

2

Simplify each side

Distribute and combine like terms on each side. 3x + 15 = 27

3

Move the constant

Subtract 15 from both sides. 3x = 12

4

Divide by the coefficient

Divide both sides by 3 to get x by itself. x = 4

EX 3hard

Solve 2(x - 5) = -16

1

The equation

Solve for x — find the value that makes both sides equal. 2(x - 5) = -16

2

Simplify each side

Distribute and combine like terms on each side. 2x - 10 = -16

3

Move the constant

Add 10 to both sides. 2x = -6

4

Divide by the coefficient

Divide both sides by 2 to get x by itself. x = -3

04 / COMMON TRAPS

Where students slip.

Trap

Skipping a tidy-up step.

Fix

Distribute and combine before moving terms.

Trap

Losing track mid-solve.

Fix

Write each step; keep it neat.

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 + 3) = 16

Need a hint?
  • Distribute and combine first.
  • Then collect, move, and divide.
C2

Solve 4(x + 1) = 28

Need a hint?
  • Distribute and combine first.
  • Then collect, move, and divide.
C3

Solve 3(x + 1) = 18

Need a hint?
  • Distribute and combine first.
  • Then collect, move, and divide.
C4

Solve 3(x + 5) = 21

Need a hint?
  • Distribute and combine first.
  • Then collect, move, and divide.
Apply

Apply (4)

A1

Solve 2(x - 1) = 6

Need a hint?
  • Distribute and combine first.
  • Then collect, move, and divide.
A2

Solve 4(x - 5) = 0

Need a hint?
  • Distribute and combine first.
  • Then collect, move, and divide.
A3

Solve 3(x + 2) = 27

Need a hint?
  • Distribute and combine first.
  • Then collect, move, and divide.
A4

Solve 4(x + 3) = -4

Need a hint?
  • Distribute and combine first.
  • Then collect, move, and divide.
Extension

Extension (4)

E1

Solve 3(x - 5) = -9

Need a hint?
  • Distribute and combine first.
  • Then collect, move, and divide.
E2

Solve 2(x - 1) = 12

Need a hint?
  • Distribute and combine first.
  • Then collect, move, and divide.
E3

Solve 2(x - 1) = 12

Need a hint?
  • Distribute and combine first.
  • Then collect, move, and divide.
E4

Solve 2(x - 5) = 2

Need a hint?
  • Distribute and combine first.
  • Then collect, move, and divide.