1
Question
Solve the following inequality:
(|x−1|−3)(|x+2|−5)<0.
(|x−1|−3)(|x+2|−5)<0.
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Solution
(|x−1|−3)(|x+2|−5)<0
x−1≥0:x≥1,|x−1|=x−1
x−1<0:x<1,|x−1|=−(x−1)
x+2≥0:x≥−2,|x+2|=x+2
x+2<0:x<−2,|x+2|=−(x+2)
x<−2, −2≤x<1, x≥1
−7<x<−2orNoSolutionor3<x<4
−7<x<−2or3<x<4
(|x−1|−3)(|x+2|−5)<0
x−1≥0:x≥1,|x−1|=x−1
x−1<0:x<1,|x−1|=−(x−1)
x+2≥0:x≥−2,|x+2|=x+2
x+2<0:x<−2,|x+2|=−(x+2)
x<−2, −2≤x<1, x≥1
−7<x<−2orNoSolutionor3<x<4
−7<x<−2or3<x<4
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