Solve an inequality like an equation, but remember the sign rule: multiplying or dividing by a negative number reverses the inequality. 6x + 7 < 2x − 25 gives 4x < −32, so x < −8.
A double inequality like 12 ≤ 2n + 6 < 18 is solved by doing the same to all three parts: subtract 6 to get 6 ≤ 2n < 12, then divide by 2 to get 3 ≤ n < 6. The integers that fit are 3, 4 and 5.
Worked example
Solve −9x + 6 ≥ −2x + 62
- Add 9x and subtract 62: −56 ≥ 7x.
- Divide by 7: −8 ≥ x.
Answer:x ≤ −8
Key words
- inequality
- a statement with <, >, ≤ or ≥
- integer
- a whole number
- double inequality
- a value between two limits
Practise this
New questions every time.
Common Core-referenced: HSA-REI.B.3