x 3 x + 3 = 8 Come play with numbers!
Integers in algebra

Why does taking away a debt feel like a gift?

# Minus a minus Two minuses in a row make a plus. `5 − (−2) = 5 + 2 = 7` Think: taking away a debt is like giving money. ## Equations `x − (−3) = 8` is the same as `x + 3 = 8` so `x = 5` ## Signs when combining - Same signs multiply → positive: `(−2)×(−3) = 6` - Different signs → negative: `(−2)×3 = −6` > Slow down at double signs. Rewrite `− (− )` as `+` first, then continue. ## Always rewrite double signs before you continue Train your hand: `a − (−b)` → `a + b` `a + (−b)` → `a − b` Do this as a separate written line. Students who “do it in their head” drop a sign. ### Multiply / divide signs - + × + = + - − × − = + - + × − = − - − × + = − Same story for division. ### Debt story You owe ₹2 (that is −2). Someone “takes away” that debt. You are ₹2 richer. 5 − (−2) = 7.

By the end of this lesson

Rewrite a minus-a-minus as plus, then finish the equation; multiply signs correctly.

Remember

  • Two minuses in a row make a plus: 5 − (−2) = 5 + 2 = 7.
  • Taking away a debt is like giving money.
  • x − (−3) = 8 is the same as x + 3 = 8, so x = 5.
  • Same signs multiply positive: (−2)×(−3) = 6.
  • Different signs multiply negative: (−2)×3 = −6.

Worked examples

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

Example 1 — Rewrite first

x − (−3) = 8

  1. Rewrite − (−3) as + 3.
  2. x + 3 = 8
  3. x = 5
  4. Check: 5 − (−3) = 5 + 3 = 8 ✓

Answer: x = 5

Check: Never solve until the double minus is rewritten.

Example 2 — Arithmetic warm-up

Compute 5 − (−2) and −4 − (−1).

  1. 5 − (−2) = 5 + 2 = 7
  2. −4 − (−1) = −4 + 1 = −3

Answer: 7 and −3

Check: Rewrite, then add.

Example 3 — Sign of a product

(−2)×(−3) and (−2)×3

  1. Same signs → +6
  2. Different signs → −6

Answer: 6 and −6

Check: Count minuses: even → positive, odd → negative.

Common mistakes

Slip 5 − (−2) = 3 (treating both minuses as one subtract).

Fix Minus a minus is plus: 7.

Rewrite before you compute.

Slip x − (−3) = 8 → x − 3 = 8 → x = 11

Fix The inner minus flips: x + 3 = 8, x = 5.

Write the rewrite on its own line.

Slip (−2)×(−3) = −6

Fix Two minuses in a multiply make plus.

Even number of minus signs.

Try on paper first

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

1. 9 − (−4) =

Answer: 13

2. x − (−6) = 10 → x =

Answer: 4

3. (−5)×(−2) =

Answer: 10

4. (−5)×2 =

Answer: −10

Touch practice

8 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

Cancelling a ₹2 debt.

Connect

Minus a minus in code: -(-2).

⭐ Star quiz

9 questions

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