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Question
Solve the inequation:
– 8 ≤ – (3x – 5) < 13
Solution
– 8 ≤ – (3x – 5) < 13
Multiplying by − 1 throughout (so inequality sign changes)
∴ 8 ≥ 3x – 5 > – 13
i.e., – 13 < 3x – 5 ≤ 8
Adding 5 on both the sides, we get
– 8 < 3x ≤ 13
Dividing, by 3 on both sides, we get
∴ `-8/3 < "x" ≤ 13/3`
i.e., x takes all real values between `-8/3` and `13/3` including `13/3`.
∴ the solution set is `[-8/3,13/3]`
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