Simplifying · One Variable · B3

Like vs unlike.

Like terms have the same variable part: 3x and 7x are like. 3x and 7 are unlike — one has an x, one does not. You can only combine like terms.

01 / THE IDEA

See it simplify.

See the like terms

Same colour = like terms.

3x
5
2x

All the terms, mixed up.

Watch it simplify

Like vs unlike terms

3x and 7x are like (both "x"); 3x and 7 are not.

1 / 2
3x+5+2x3x + 5 + 2x
1

Group like terms

Gather the terms that share the same variable part.

(3x+2x)+5(3x + 2x) + 5
2

Combine

Add the coefficients within each group.

5x+55x + 5
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
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— / WHY IT WORKS

The idea underneath.

What makes terms alike

Like terms share the exact variable part. 3x and 7x are alike; 3x and 7 are not (one is an x-term, one is a number). Unlike terms just sit side by side.

Why it works

You can add apples to apples, not apples to oranges.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

5x + 11 + 6x

1

Group like terms

Gather the terms that share the same variable part. → (5x + 6x) + 11

2

Combine

Add the coefficients within each group. → 11x + 11

EX 2medium

3x + 11 + 5x

1

Group like terms

Gather the terms that share the same variable part. → (3x + 5x) + 11

2

Combine

Add the coefficients within each group. → 8x + 11

EX 3hard

11x + 14 + 6x

1

Group like terms

Gather the terms that share the same variable part. → (11x + 6x) + 14

2

Combine

Add the coefficients within each group. → 17x + 14

04 / COMMON TRAPS

Where students slip.

Trap

3x + 5 = 8x.

Fix

Unlike — leave it as 3x + 5.

Trap

Combining a number with an x-term.

Fix

Numbers and x-terms are different kinds.

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 + 11 + 6x

Need a hint?
  • Look at the variable part only.
  • A number is not an x-term.
C2

Simplify 6x + 7 + 2x

Need a hint?
  • Look at the variable part only.
  • A number is not an x-term.
C3

Simplify 3x + 5 + 6x

Need a hint?
  • Look at the variable part only.
  • A number is not an x-term.
C4

Simplify 4x + 2 + 6x

Need a hint?
  • Look at the variable part only.
  • A number is not an x-term.
Apply

Apply (4)

A1

Simplify 3x + 11 + 5x

Need a hint?
  • Look at the variable part only.
  • A number is not an x-term.
A2

Simplify 7x + 6 + 4x

Need a hint?
  • Look at the variable part only.
  • A number is not an x-term.
A3

Simplify 4x + 11 + 5x

Need a hint?
  • Look at the variable part only.
  • A number is not an x-term.
A4

Simplify 8x + 8 + 9x

Need a hint?
  • Look at the variable part only.
  • A number is not an x-term.
Extension

Extension (4)

E1

Simplify 11x + 14 + 6x

Need a hint?
  • Look at the variable part only.
  • A number is not an x-term.
E2

Simplify 12x + 13 + 4x

Need a hint?
  • Look at the variable part only.
  • A number is not an x-term.
E3

Simplify 10x + 12 + 6x

Need a hint?
  • Look at the variable part only.
  • A number is not an x-term.
E4

Simplify 7x + 5 + 10x

Need a hint?
  • Look at the variable part only.
  • A number is not an x-term.