Simplifying · One Variable · B5

Keep constants separate.

When an expression mixes x-terms and numbers, collect the x-terms together and leave the constant by itself. 2x + 5 + 4x = 6x + 5.

01 / THE IDEA

See it simplify.

See the like terms

Same colour = like terms.

2x
5
4x

All the terms, mixed up.

Watch it simplify

Keep constants separate

2x + 5 + 4x: combine 2x and 4x into 6x; the 5 stays.

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2x+5+4x2x + 5 + 4x
1

Group like terms

Gather the terms that share the same variable part.

(2x+4x)+5(2x + 4x) + 5
2

Combine

Add the coefficients within each group.

6x+56x + 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.

Two kinds, kept apart

x-terms combine with x-terms; numbers stay as numbers. 2x + 5 + 4x = 6x + 5. Write the variable term first, then the constant.

Why it works

Sort the x-tiles into one pile; the number stays in its own pile.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

3x + 11 + 4x

1

Group like terms

Gather the terms that share the same variable part. → (3x + 4x) + 11

2

Combine

Add the coefficients within each group. → 7x + 11

EX 2medium

9x + 13 + 7x

1

Group like terms

Gather the terms that share the same variable part. → (9x + 7x) + 13

2

Combine

Add the coefficients within each group. → 16x + 13

EX 3hard

4x + 13 + 4x

1

Group like terms

Gather the terms that share the same variable part. → (4x + 4x) + 13

2

Combine

Add the coefficients within each group. → 8x + 13

04 / COMMON TRAPS

Where students slip.

Trap

2x + 5 + 4x = 11x.

Fix

The 5 is a number, not an x — it cannot join the xs.

Trap

Forgetting the constant entirely.

Fix

It stays in the answer: 6x + 5.

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 3x + 11 + 4x

Need a hint?
  • Combine only the x-terms.
  • Write the constant after, unchanged.
C2

Simplify 2x + 6 + 4x

Need a hint?
  • Combine only the x-terms.
  • Write the constant after, unchanged.
C3

Simplify 2x + 9 + 2x

Need a hint?
  • Combine only the x-terms.
  • Write the constant after, unchanged.
C4

Simplify 6x + 10 + 3x

Need a hint?
  • Combine only the x-terms.
  • Write the constant after, unchanged.
Apply

Apply (4)

A1

Simplify 9x + 13 + 7x

Need a hint?
  • Combine only the x-terms.
  • Write the constant after, unchanged.
A2

Simplify 6x + 11 + 6x

Need a hint?
  • Combine only the x-terms.
  • Write the constant after, unchanged.
A3

Simplify 8x + 9 + 6x

Need a hint?
  • Combine only the x-terms.
  • Write the constant after, unchanged.
A4

Simplify 9x + 7 + 7x

Need a hint?
  • Combine only the x-terms.
  • Write the constant after, unchanged.
Extension

Extension (4)

E1

Simplify 4x + 13 + 4x

Need a hint?
  • Combine only the x-terms.
  • Write the constant after, unchanged.
E2

Simplify 12x + 11 + 6x

Need a hint?
  • Combine only the x-terms.
  • Write the constant after, unchanged.
E3

Simplify 12x + 10 + 8x

Need a hint?
  • Combine only the x-terms.
  • Write the constant after, unchanged.
E4

Simplify 5x + 10 + 10x

Need a hint?
  • Combine only the x-terms.
  • Write the constant after, unchanged.