Solve the absolute value inequality and graph the solution. |x - 1| $\ge$ 2

Question

Quizplus · Accepted Answer

To solve |x - 1| ≥ 2, we need to consider two cases:
Case 1: (x - 1) ≥ 0, then |x - 1| = x - 1. Hence, we have x - 1 ≥ 2, which gives x ≥ 3.
Case 2: (x - 1) < 0, then |x - 1| = -(x - 1) = -x + 1. Hence, we have -x + 1 ≥ 2, which gives x ≤ -1.
Therefore, the solution is x ≤ -1 or x ≥ 3. Graphically, this represents the entire number line except for the interval between -1 and 3. The correct graph is represented by choice B.

Solve the Absolute Value Inequality and Graph the Solution ≥\ge≥ 2 A) B) C) D)

Solve the Absolute Value Inequality and Graph the Solution $\ge$ 2
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