x 3 x + 3 = 8 Come play with numbers!
One-step equations

How do we undo groups of x?

# Undo × and ÷ Multiplication and division are opposites. To undo `× 3`, **divide by 3**. To undo `÷ 5` (or `/5`), **multiply by 5**. ## Example `3x = 18` Divide both sides by 3: `x = 6` ## Example `x/4 = 5` Multiply both sides by 4: `x = 20` ## Careful `3x` means 3 **times** x, not 3 + x. Check: `3 × 6 = 18` ✓ · `20 / 4 = 5` ✓ ## Times and share `3x = 18` says: three equal groups make 18. One group is 6. `x/4 = 5` says: when the box is shared into 4, each share is 5. The whole box is 20. ### Opposite table | Stuck to x | Do this to both sides | | --- | --- | | × 3 (written 3x) | ÷ 3 | | ÷ 5 (written x/5) | × 5 | | × 8 | ÷ 8 | ### Check is still mandatory `3x = 18` and you got 6: compute 3 × 6. If you do not get 18, you used the wrong opposite.

By the end of this lesson

Solve one-step equations that undo × or ÷, remembering that 3x means 3 times x.

Remember

  • Multiplication and division are opposites.
  • 3x = 18 → divide both sides by 3 → x = 6.
  • x/4 = 5 → multiply both sides by 4 → x = 20.
  • 3x is 3 times x, not 3 + x.
  • Never divide by zero. Dividing by 1 does nothing useful but is legal.

Worked examples

Cover the answer. Try the steps on paper, then open them.

Example 1 — Undo times

5x = 35

  1. 5x means 5 groups of x.
  2. Divide both sides by 5.
  3. x = 7
  4. Check: 5 × 7 = 35 ✓

Answer: x = 7

Check: 35 ÷ 5 = 7.

Example 2 — Undo divide

x/3 = 8

  1. x has been shared into 3.
  2. Multiply both sides by 3.
  3. x = 24
  4. Check: 24 / 3 = 8 ✓

Answer: x = 24

Check: 8 × 3 = 24.

Example 3 — Not plus

Why is the answer to 3x = 12 not x = 9?

  1. If someone does 12 − 3 they treated 3x as 3 + x.
  2. 3x is multiply.
  3. 12 ÷ 3 = 4.

Answer: x = 4

Check: Check: 3 × 4 = 12, not 3 + 9.

Common mistakes

Slip 3x = 12 → x = 9 (subtracted 3).

Fix Divide by 3: x = 4.

Hidden multiply, not plus.

Slip x/4 = 5 → x = 5/4 or x = 1.

Fix Multiply both sides by 4: x = 20.

Undo sharing by gathering 4 equal groups.

Slip 4x = 4 → x = 0 or x = 4×4.

Fix 4x = 4 → x = 1.

One group of 4 equals 4, so x is 1.

Try on paper first

Write the answer, then tap Reveal. These are not the quiz — they are warm-ups.

1. 3x = 21 → x =

Answer: 7

2. x/5 = 6 → x =

Answer: 30

3. 8x = 8 → x =

Answer: 1

4. x/2 = 0 → x =

Answer: 0

Touch practice

9 tap / type

Tap an option or type the answer. Retry any miss. Extra generated questions appear after the set if this topic allows it.

Optional picture lab

After practice

Real world

Sharing 18 sweets among 3 friends.

Connect

Division undoes multiplication in code too.

⭐ Star quiz

9 questions

Finish the touch practice first if you can. Then answer without peeking. Read every “why”.

← Undo + and − All topics →