Simplifying · One Variable · B4

Combine like terms.

To combine like terms, add their coefficients and keep the variable. 2x + 5x = 7x — two xs plus five xs makes seven xs. The variable does not change.

01 / THE IDEA

See it simplify.

See the like terms

Same colour = like terms.

2x
5x

All the terms, mixed up.

Watch it simplify

Combine like terms

2x + 5x: add the counts, 2 + 5 = 7, so 7x.

1 / 2
2x+5x2x + 5x
1

Group like terms

Gather the terms that share the same variable part.

(2x+5x)(2x + 5x)
2

Combine

Add the coefficients within each group.

7x7x
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.

Add the counts

Like terms combine by adding coefficients. 2x + 5x = 7x. The x stays an x — you are counting xs, not multiplying them.

Why it works

2 x-tiles + 5 x-tiles = 7 x-tiles.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

6x + 2x

1

Group like terms

Gather the terms that share the same variable part. → (6x + 2x)

2

Combine

Add the coefficients within each group. → 8x

EX 2medium

9x + 6x

1

Group like terms

Gather the terms that share the same variable part. → (9x + 6x)

2

Combine

Add the coefficients within each group. → 15x

EX 3hard

4x + 4x

1

Group like terms

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

2

Combine

Add the coefficients within each group. → 8x

04 / COMMON TRAPS

Where students slip.

Trap

2x + 5x = 7x² (changing the power).

Fix

The variable stays x; only the count changes.

Trap

2x + 5x = 10x (multiplying).

Fix

Add the coefficients, do not multiply them.

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 6x + 2x

Need a hint?
  • Add the numbers in front.
  • Keep the variable exactly as it is.
C2

Simplify 5x + 2x

Need a hint?
  • Add the numbers in front.
  • Keep the variable exactly as it is.
C3

Simplify 3x + 2x

Need a hint?
  • Add the numbers in front.
  • Keep the variable exactly as it is.
C4

Simplify 6x + 3x

Need a hint?
  • Add the numbers in front.
  • Keep the variable exactly as it is.
Apply

Apply (4)

A1

Simplify 9x + 6x

Need a hint?
  • Add the numbers in front.
  • Keep the variable exactly as it is.
A2

Simplify 3x + 8x

Need a hint?
  • Add the numbers in front.
  • Keep the variable exactly as it is.
A3

Simplify 6x + 6x

Need a hint?
  • Add the numbers in front.
  • Keep the variable exactly as it is.
A4

Simplify 8x + 8x

Need a hint?
  • Add the numbers in front.
  • Keep the variable exactly as it is.
Extension

Extension (4)

E1

Simplify 4x + 4x

Need a hint?
  • Add the numbers in front.
  • Keep the variable exactly as it is.
E2

Simplify 10x + 10x

Need a hint?
  • Add the numbers in front.
  • Keep the variable exactly as it is.
E3

Simplify 9x + 8x

Need a hint?
  • Add the numbers in front.
  • Keep the variable exactly as it is.
E4

Simplify 12x + 10x

Need a hint?
  • Add the numbers in front.
  • Keep the variable exactly as it is.