Solving Equations · Distribute & combine · 5.2

Combine like terms.

If a side has like terms, combine them before solving. 2x + x + 1 = 10 → 3x + 1 = 10 → 3x = 9 → x = 3.

01 / THE IDEA

See it work.

Watch the method

Combine like terms

2x + x + 1 = 10 → 3x + 1 = 10 → x = 3.

1 / 4
2x+x+1=102x + x + 1 = 10
1

The equation

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

2x+x+1=102x + x + 1 = 10
2

Simplify each side

Distribute and combine like terms on each side.

3x+1=103x + 1 = 10
3

Move the constant

Subtract 1 from both sides.

3x=93x = 9
4

Divide by the coefficient

Divide both sides by 3 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.

Tidy first

Add the x terms together and the constants together on each side before applying inverse operations.

Why it works

2x + x = 3x.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Solve 1x + 8 + 2x = 23

1

The equation

Solve for x — find the value that makes both sides equal. 1x + 8 + 2x = 23

2

Simplify each side

Distribute and combine like terms on each side. 3x + 8 = 23

3

Move the constant

Subtract 8 from both sides. 3x = 15

4

Divide by the coefficient

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

EX 2medium

Solve 3x - 3 + 4x = 18

1

The equation

Solve for x — find the value that makes both sides equal. 3x - 3 + 4x = 18

2

Simplify each side

Distribute and combine like terms on each side. 7x - 3 = 18

3

Move the constant

Add 3 to both sides. 7x = 21

4

Divide by the coefficient

Divide both sides by 7 to get x by itself. x = 3

EX 3hard

Solve 2x + 2 + 3x = 27

1

The equation

Solve for x — find the value that makes both sides equal. 2x + 2 + 3x = 27

2

Simplify each side

Distribute and combine like terms on each side. 5x + 2 = 27

3

Move the constant

Subtract 2 from both sides. 5x = 25

4

Divide by the coefficient

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

04 / COMMON TRAPS

Where students slip.

Trap

Combining unlike terms.

Fix

Only x terms combine with x terms.

Trap

Solving before tidying.

Fix

Combine like terms first.

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 3x - 5 + 4x = 30

Need a hint?
  • Add the x terms together.
  • Then solve the two-step.
C2

Solve 3x - 4 + 3x = 8

Need a hint?
  • Add the x terms together.
  • Then solve the two-step.
C3

Solve 2x - 1 + 2x = 27

Need a hint?
  • Add the x terms together.
  • Then solve the two-step.
C4

Solve 3x - 3 + 4x = 11

Need a hint?
  • Add the x terms together.
  • Then solve the two-step.
Apply

Apply (4)

A1

Solve 1x - 6 + 1x = 6

Need a hint?
  • Add the x terms together.
  • Then solve the two-step.
A2

Solve 1x + 5 + 1x = 21

Need a hint?
  • Add the x terms together.
  • Then solve the two-step.
A3

Solve 1x + 2 + 4x = 12

Need a hint?
  • Add the x terms together.
  • Then solve the two-step.
A4

Solve 3x + 4 + 3x = 16

Need a hint?
  • Add the x terms together.
  • Then solve the two-step.
Extension

Extension (4)

E1

Solve 1x + 5 + 1x = 11

Need a hint?
  • Add the x terms together.
  • Then solve the two-step.
E2

Solve 4x - 3 + 3x = 25

Need a hint?
  • Add the x terms together.
  • Then solve the two-step.
E3

Solve 3x + 2 + 4x = 44

Need a hint?
  • Add the x terms together.
  • Then solve the two-step.
E4

Solve 2x + 1 + 4x = 49

Need a hint?
  • Add the x terms together.
  • Then solve the two-step.