Simplifying · One Variable · B6

Subtract like terms.

Subtracting like terms subtracts the coefficients. 8x − 3x = 5x. Remember the invisible 1: 6x − x = 6x − 1x = 5x.

01 / THE IDEA

See it simplify.

See the like terms

Same colour = like terms.

8x
-3x

All the terms, mixed up.

Watch it simplify

Subtract like terms

8x − 3x = 5x; and x counts as 1x, so 6x − x = 5x.

1 / 2
8x−3x8x - 3x
1

Group like terms

Gather the terms that share the same variable part.

(8x−3x)(8x - 3x)
2

Combine

Add the coefficients within each group.

5x5x
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Simplify it.

Type the simplest form (e.g. 6x + 5). Use ^ for powers.

streak 0
best 0
… =
— / WHY IT WORKS

The idea underneath.

Take some away

Subtract the counts: 8x − 3x = 5x. A lone x is 1x, so 6x − x = 5x, not 6x.

Why it works

Remove 3 x-tiles from 8 x-tiles, 5 remain.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

10x - 7x

1

Group like terms

Gather the terms that share the same variable part. → (10x - 7x)

2

Combine

Add the coefficients within each group. → 3x

EX 2medium

12x - 4x

1

Group like terms

Gather the terms that share the same variable part. → (12x - 4x)

2

Combine

Add the coefficients within each group. → 8x

EX 3hard

15x - 12x

1

Group like terms

Gather the terms that share the same variable part. → (15x - 12x)

2

Combine

Add the coefficients within each group. → 3x

04 / COMMON TRAPS

Where students slip.

Trap

6x − x = 6x (treating x as 0x).

Fix

x is 1x, so 6x − x = 5x.

Trap

6x − x = 6.

Fix

You keep the x: the answer is 5x.

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

Simplify 10x - 7x

Need a hint?
  • Subtract the coefficients.
  • A lone x is 1x.
C2

Simplify 8x - 2x

Need a hint?
  • Subtract the coefficients.
  • A lone x is 1x.
C3

Simplify 8x - 5x

Need a hint?
  • Subtract the coefficients.
  • A lone x is 1x.
C4

Simplify 10x - 6x

Need a hint?
  • Subtract the coefficients.
  • A lone x is 1x.
Apply

Apply (4)

A1

Simplify 12x - 4x

Need a hint?
  • Subtract the coefficients.
  • A lone x is 1x.
A2

Simplify 8x - 5x

Need a hint?
  • Subtract the coefficients.
  • A lone x is 1x.
A3

Simplify 9x - 1x

Need a hint?
  • Subtract the coefficients.
  • A lone x is 1x.
A4

Simplify 6x - 4x

Need a hint?
  • Subtract the coefficients.
  • A lone x is 1x.
Extension

Extension (4)

E1

Simplify 15x - 12x

Need a hint?
  • Subtract the coefficients.
  • A lone x is 1x.
E2

Simplify 13x - 4x

Need a hint?
  • Subtract the coefficients.
  • A lone x is 1x.
E3

Simplify 10x - 4x

Need a hint?
  • Subtract the coefficients.
  • A lone x is 1x.
E4

Simplify 11x - 10x

Need a hint?
  • Subtract the coefficients.
  • A lone x is 1x.