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

Can a box hold a number below zero?

# Negatives are allowed The mystery box can hold **negative** numbers. Number line: … −3, −2, −1, 0, 1, 2, 3 … `x + 5 = 2` Subtract 5: `x = −3` Check: `−3 + 5 = 2` ✓ ## Walk the line Start at 2. Walk 5 steps left (because we undo +5). You land on −3. Negatives are not “wrong answers”. Temperature, lifts, and cricket run-rates use them. ## The number line is your friend Draw this once in your notebook and keep it: ``` ←——|——|——|——|——|——|——|——|——→ −3 −2 −1 0 1 2 3 4 ``` Adding a positive number walks **right**. Subtracting a positive number walks **left**. `x + 5 = 2` means: “from x, walk 5 right and you land on 2.” So x must be 5 left of 2, which is −3. ### Negatives are ordinary A fridge at −3 °C is not a broken fridge. A lift at −1 is the basement. Your mystery box can hold those numbers.

By the end of this lesson

Solve one-step equations whose solution is negative, and check on a number line.

Remember

  • x is allowed to be negative. Negatives are not “wrong answers”.
  • x + 5 = 2 → x = −3, because −3 + 5 = 2.
  • On a number line, undo +5 by walking 5 steps left from 2.
  • Temperature, basement floors, and debts use negatives every day.
  • Write the minus sign large and close to the digit: −3, not a floating dash.

Worked examples

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

Example 1 — Walk left

x + 5 = 2

  1. Subtract 5 from both sides.
  2. 2 − 5 = −3
  3. Check: −3 + 5 = 2 ✓

Answer: x = −3

Check: Start at 2, five left, land on −3.

Example 2 — Already on the left

x + 1 = 0

  1. Subtract 1.
  2. x = −1
  3. Check: −1 + 1 = 0 ✓

Answer: x = −1

Check: A number plus 1 makes 0, so the number is −1.

Example 3 — Undo minus into a negative

x − 4 = −9

  1. Add 4 to both sides.
  2. −9 + 4 = −5
  3. Check: −5 − 4 = −9 ✓

Answer: x = −5

Check: Negatives on both sides are fine.

Common mistakes

Slip x + 5 = 2 → x = 7 (added instead of subtracted).

Fix Undo +5 by subtracting: 2 − 5 = −3.

Opposite, even if the answer looks “less nice”.

Slip Refusing −3 because “answers must be positive”.

Fix The check −3 + 5 = 2 proves it.

Positive is not a rule.

Slip Writing 2 − 5 as 5 − 2 = 3.

Fix Order matters: 2 − 5 is −3.

Start at 2, not at 5.

Try on paper first

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

1. x + 8 = 3 → x =

Answer: −5

2. x + 1 = −4 → x =

Answer: −5

3. x − 2 = −6 → x =

Answer: −4

4. −3 + 5 =

Answer: 2

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

Temperature and basement floors.

Connect

Signed numbers in games (lives, scores).

⭐ Star quiz

9 questions

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

← Unit Minus a minus →