Simplifying · One Variable · B1

A variable is a number.

A variable is just a letter standing in for a number we do not know yet. x + 4 is an instruction: whatever x is, add 4. It is not a fixed special object.

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

A variable is a number

x can be any number; x + 4 just says "add 4 to it".

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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
best 0
… =
— / WHY IT WORKS

The idea underneath.

The unknown

x represents some number. An expression in x is a rule that works for every value of x. If x = 5, then x + 4 = 9; if x = 10, x + 4 = 14.

Why it works

x is a box; whatever number you put in, the expression tells you what to do.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

6x + 4x

1

Group like terms

Gather the terms that share the same variable part. → (6x + 4x)

2

Combine

Add the coefficients within each group. → 10x

EX 2medium

4x + 3x

1

Group like terms

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

2

Combine

Add the coefficients within each group. → 7x

EX 3hard

6x + 11x

1

Group like terms

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

2

Combine

Add the coefficients within each group. → 17x

04 / COMMON TRAPS

Where students slip.

Trap

"x" is one specific secret number.

Fix

x can be anything; the expression works for all values.

Trap

x means multiply.

Fix

x is a variable here, not the × sign.

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 6x + 4x

Need a hint?
  • Replace x with a number to see what the expression does.
  • The rule works for every value of x.
C2

Simplify 2x + 2x

Need a hint?
  • Replace x with a number to see what the expression does.
  • The rule works for every value of x.
C3

Simplify 4x + 3x

Need a hint?
  • Replace x with a number to see what the expression does.
  • The rule works for every value of x.
C4

Simplify 6x + 2x

Need a hint?
  • Replace x with a number to see what the expression does.
  • The rule works for every value of x.
Apply

Apply (4)

A1

Simplify 4x + 3x

Need a hint?
  • Replace x with a number to see what the expression does.
  • The rule works for every value of x.
A2

Simplify 6x + 7x

Need a hint?
  • Replace x with a number to see what the expression does.
  • The rule works for every value of x.
A3

Simplify 4x + 9x

Need a hint?
  • Replace x with a number to see what the expression does.
  • The rule works for every value of x.
A4

Simplify 3x + 3x

Need a hint?
  • Replace x with a number to see what the expression does.
  • The rule works for every value of x.
Extension

Extension (4)

E1

Simplify 6x + 11x

Need a hint?
  • Replace x with a number to see what the expression does.
  • The rule works for every value of x.
E2

Simplify 6x + 8x

Need a hint?
  • Replace x with a number to see what the expression does.
  • The rule works for every value of x.
E3

Simplify 5x + 7x

Need a hint?
  • Replace x with a number to see what the expression does.
  • The rule works for every value of x.
E4

Simplify 5x + 5x

Need a hint?
  • Replace x with a number to see what the expression does.
  • The rule works for every value of x.