Simplifying · One Variable · B2

The coefficient.

The number in front of a variable is its coefficient. 3x means x + x + x. A lone x has coefficient 1, not 0. The coefficient is the count of that variable.

01 / THE IDEA

See it simplify.

See the like terms

Same colour = like terms.

2x
3x

All the terms, mixed up.

Watch it simplify

The coefficient

3x is three copies of x; x by itself is 1x.

1 / 2
2x+3x2x + 3x
1

Group like terms

Gather the terms that share the same variable part.

(2x+3x)(2x + 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.

How many xs

3x = x + x + x. The coefficient tells you how many. x means 1x. This is why combining like terms is just adding the counts.

Why it works

3x is "3 of the x-tiles".

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

5x + 3x

1

Group like terms

Gather the terms that share the same variable part. → (5x + 3x)

2

Combine

Add the coefficients within each group. → 8x

EX 2medium

3x + 3x

1

Group like terms

Gather the terms that share the same variable part. → (3x + 3x)

2

Combine

Add the coefficients within each group. → 6x

EX 3hard

7x + 12x

1

Group like terms

Gather the terms that share the same variable part. → (7x + 12x)

2

Combine

Add the coefficients within each group. → 19x

04 / COMMON TRAPS

Where students slip.

Trap

A lone x has coefficient 0.

Fix

It is 1x — one copy of x.

Trap

3x means 3 + x.

Fix

It means 3 × x.

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 5x + 3x

Need a hint?
  • The coefficient is the count in front.
  • x means 1x.
C2

Simplify 2x + 3x

Need a hint?
  • The coefficient is the count in front.
  • x means 1x.
C3

Simplify 3x + 3x

Need a hint?
  • The coefficient is the count in front.
  • x means 1x.
C4

Simplify 3x + 4x

Need a hint?
  • The coefficient is the count in front.
  • x means 1x.
Apply

Apply (4)

A1

Simplify 3x + 3x

Need a hint?
  • The coefficient is the count in front.
  • x means 1x.
A2

Simplify 3x + 6x

Need a hint?
  • The coefficient is the count in front.
  • x means 1x.
A3

Simplify 3x + 3x

Need a hint?
  • The coefficient is the count in front.
  • x means 1x.
A4

Simplify 9x + 7x

Need a hint?
  • The coefficient is the count in front.
  • x means 1x.
Extension

Extension (4)

E1

Simplify 7x + 12x

Need a hint?
  • The coefficient is the count in front.
  • x means 1x.
E2

Simplify 10x + 10x

Need a hint?
  • The coefficient is the count in front.
  • x means 1x.
E3

Simplify 12x + 7x

Need a hint?
  • The coefficient is the count in front.
  • x means 1x.
E4

Simplify 5x + 8x

Need a hint?
  • The coefficient is the count in front.
  • x means 1x.