Simplifying · One Variable · B12

One-variable mastery.

Put it together: any one-variable expression simplifies by distributing brackets, then collecting like terms, keeping every sign.

01 / THE IDEA

See it simplify.

Watch it simplify

One-variable mastery

Distribute, then collect — carefully with signs.

1 / 3
5x−2(x−1)5x - 2(x - 1)
1

Distribute

Multiply out the brackets — every term inside by the factor in front.

5x−2x+25x - 2x + 2
2

Group like terms

Gather the terms that share the same variable part.

(5x−2x)+2(5x - 2x) + 2
3

Combine

Add the coefficients within each group.

3x+23x + 2
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Simplify it.

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

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— / WHY IT WORKS

The idea underneath.

The one-variable method

Expand brackets (watch negatives) → gather x-terms → gather constants → write variable term then constant.

Why it works

Same recipe, mixed ingredients.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

5x - 2x

1

Group like terms

Gather the terms that share the same variable part. → (5x - 2x)

2

Combine

Add the coefficients within each group. → 3x

EX 2medium

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. → 2x

EX 3hard

5(x + 11) + 12x

1

Distribute

Multiply out the brackets — every term inside by the factor in front. → 5x + 55 + 12x

2

Group like terms

Gather the terms that share the same variable part. → (5x + 12x) + 55

3

Combine

Add the coefficients within each group. → 17x + 55

04 / COMMON TRAPS

Where students slip.

Trap

Sign slips under a negative bracket.

Fix

Distribute the minus to every term first.

Trap

Leaving like terms uncombined.

Fix

Collect fully — the pad rejects half-done answers.

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 - 2x

Need a hint?
  • Distribute, then collect.
  • Track every sign.
C2

Simplify 8x - 7x

Need a hint?
  • Distribute, then collect.
  • Track every sign.
C3

Simplify 4(x + 3) + 3x

Need a hint?
  • Distribute, then collect.
  • Track every sign.
C4

Simplify 9x - 4x

Need a hint?
  • Distribute, then collect.
  • Track every sign.
Apply

Apply (4)

A1

Simplify 5x - 3x

Need a hint?
  • Distribute, then collect.
  • Track every sign.
A2

Simplify 9x + 10 + 9x

Need a hint?
  • Distribute, then collect.
  • Track every sign.
A3

Simplify 4(x + 5) + 7x

Need a hint?
  • Distribute, then collect.
  • Track every sign.
A4

Simplify 3x + 14 + 6x

Need a hint?
  • Distribute, then collect.
  • Track every sign.
Extension

Extension (4)

E1

Simplify 5(x + 11) + 12x

Need a hint?
  • Distribute, then collect.
  • Track every sign.
E2

Simplify 7x + 6 + 10x

Need a hint?
  • Distribute, then collect.
  • Track every sign.
E3

Simplify 10x + 9 + 7x

Need a hint?
  • Distribute, then collect.
  • Track every sign.
E4

Simplify 6(x + 4) + 12x

Need a hint?
  • Distribute, then collect.
  • Track every sign.