Engineering Board Exam Reviewer · Inequalities and Absolute Value · hard

Find the sum of all solutions of |x-1|+|x+2|=5.

1. 1
2. -1
3. 5
4. -5

Answer

B. -1

Solution

Case x≥1: 2x+1=5 x=2. Case -2≤ x<1: 3=5, impossible. Case x<-2: -2x-1=5 x=-3. The solutions are 2 and -3, with sum -1.

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