Simplifying · One Variable · B7

Negative coefficients.

If you subtract a bigger like term, the coefficient becomes negative: 3x − 8x = −5x. Order the terms but keep every sign.

01 / THE IDEA

See it simplify.

See the like terms

Same colour = like terms.

3x
-8x

All the terms, mixed up.

Watch it simplify

Negative coefficients

3x − 8x: 3 − 8 = −5, so −5x.

1 / 2
3x−8x3x - 8x
1

Group like terms

Gather the terms that share the same variable part.

(3x−8x)(3x - 8x)
2

Combine

Add the coefficients within each group.

−5x-5x
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.

Counts below zero

Coefficients follow the number line. 3x − 8x = −5x. And −2x + 7x = 5x. Treat each term as its signed coefficient times x.

Why it works

Owe 8 xs, have 3 → you are 5 xs short: −5x.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

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. → 0

EX 2medium

7x - 6x

1

Group like terms

Gather the terms that share the same variable part. → (7x - 6x)

2

Combine

Add the coefficients within each group. → x

EX 3hard

7x - 11x

1

Group like terms

Gather the terms that share the same variable part. → (7x - 11x)

2

Combine

Add the coefficients within each group. → -4x

04 / COMMON TRAPS

Where students slip.

Trap

3x − 8x = 5x (wrong sign).

Fix

It is −5x; 3 − 8 = −5.

Trap

Dropping the leading minus.

Fix

Keep it: the answer is −5x.

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 - 3x

Need a hint?
  • Combine the signed coefficients.
  • A negative result keeps its minus.
C2

Simplify 2x - 2x

Need a hint?
  • Combine the signed coefficients.
  • A negative result keeps its minus.
C3

Simplify 6x - 4x

Need a hint?
  • Combine the signed coefficients.
  • A negative result keeps its minus.
C4

Simplify 3x - 5x

Need a hint?
  • Combine the signed coefficients.
  • A negative result keeps its minus.
Apply

Apply (4)

A1

Simplify 7x - 6x

Need a hint?
  • Combine the signed coefficients.
  • A negative result keeps its minus.
A2

Simplify 8x - 4x

Need a hint?
  • Combine the signed coefficients.
  • A negative result keeps its minus.
A3

Simplify 9x - 3x

Need a hint?
  • Combine the signed coefficients.
  • A negative result keeps its minus.
A4

Simplify 4x - 9x

Need a hint?
  • Combine the signed coefficients.
  • A negative result keeps its minus.
Extension

Extension (4)

E1

Simplify 7x - 11x

Need a hint?
  • Combine the signed coefficients.
  • A negative result keeps its minus.
E2

Simplify 5x - 9x

Need a hint?
  • Combine the signed coefficients.
  • A negative result keeps its minus.
E3

Simplify 4x - 5x

Need a hint?
  • Combine the signed coefficients.
  • A negative result keeps its minus.
E4

Simplify 7x - 4x

Need a hint?
  • Combine the signed coefficients.
  • A negative result keeps its minus.