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Question
Answer the following:
Solve the following for x, where |x| is modulus function, [x] is greatest interger function, {x} is a fractional part function
1 < |x − 1| < 4
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Solution
1 < |x − 1| < 4
If x ≥ 1, Ix − 1| = x − 1
If x < 1, lx − 1| = 1 − x
∴ 1 < x − 1 < 4 or 1 < 1 − x < 4
∴ 2 < x < 5 or 0 < − x < 3
∴ 2 < x < 5 or 0 > x > −3
∴ x ∈ (2, 5) or x ∈ (−3, 0)
∴ the solution set is (−3, 0) ∪ (2 ,5).
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