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Question
Solve the following for x, where |x| is modulus function, [x] is greatest integer function, [x] is a fractional part function.
|x + 4| ≥ 5
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Solution
|x + 4| ≥ 5
The solution of |x| ≥ a is x ≤ -a or x ≥ a
∴ |x + 4| ≥ 5 ...[Given]
∴ x + 4 ≤ -5 or x + 4 ≥ 5
∴ x ≤ -5 – 4 or x ≥ 5 – 4
∴ x ≤ -9 or x ≥ 1
∴ The solution set = (-∞, – 9] ∪ [1, ∞)
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