Michigan State University - Diagnostic Exam

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2.13

  •   Solve the inequality |x + 3| ≥ 1 for x.

     

    a) x ≤ - 2 b) - 4 ≤ x ≤ - 2 c) x ≥ - 2
       
    d) - 4 ≥ x ≥ - 2 e) x ≥ - 2 or x ≤ - 4

Solution:
⇒±(x + 3) ≥ 1 . So we have two cases:

x+3≥1 ⇒ x ≥ - 2 or


-(x+3) ≥ 1 ⇒ x + 3 ≤ - 1 ⇒ x ≤ - 4

Diagnostic:

See 1.17: Inequalities (Absolute Value) .

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July 15, 2008