Question

What is the solution to the inequality 3x - 12| ≥ 6?

0-6 02 Ox<-6 or x> 18
Ox≤2 or x ≥6

Answer 1

Answer: x ≤ 2 or x ≥ 6

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Work Shown:

|3x-12| ≥ 6

3x-12 ≥ 6 or 3x-12 ≤ -6 ..... see note below

3x ≥ 6+12 or 3x ≤ -6+12

3x ≥ 18 or 3x ≤ -6+12

3x ≥ 18 or 3x ≤ 6

x ≥ 18/3 or x ≤ 6/3

x ≥ 6 or x ≤ 2

x ≤ 2 or x ≥ 6

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Note: if |A| ≥ B, then A ≥ B or A ≤ -B where B is some positive number.

Example: |x| ≥ 5 means either x ≥ 5 or x ≤ - 5