Question

What is the solution to |x-6| ≥ 5?

A. 1 ≤x≤11
B. -11 ≤x≤ 1
C. X≥ 11 or x≤ 1
D. X≥ 1 or x≤ -11

Answer 1

|x−6|≥5

We know either x−6 ≥ 5 or x−6≤−5.

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x − 6 ≥ 5 (Possibility 1)

x−6 + 6≥5 + 6 (Add 6 to both sides)

x ≥ 11

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x−6≤−5 (Possibility 2)

x − 6 + 6 ≤ −5 + 6 (Add 6 to both sides)

x ≤ 1

Answer: x ≥ 11 or x ≤ 1. Option "C".