Determine the values of x for which the inequality ||x - 5| - 3| > 2 holds true.

Answer Choices

Correct answer marked below

( -∞, 0) or (4, 6) or ( 10, ∞)

Correct

( -∞, -1) or (1, 7) or ( 12, ∞)

( -∞, -1) or ( 12, ∞)

( -∞, 7) or ( 12, ∞)

( -∞, -1) or (1, 3) or ( 12, ∞)

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Explanation

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Official Explanation

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When x = 5, we check the inequality: ||5 - 5| - 3| > 2. This simplifies to ||0| - 3| > 2, which becomes |0 - 3| > 2, or 3 > 2 (true). Therefore, we can eliminate options C and E since they do not include x = 5. Next, we test x = 2: ||2…

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What this question tests

What it tests

Your ability to solve and combine linear inequalities and reason about ranges of values.

Common trap

Failing to flip the inequality sign when multiplying or dividing by a negative, or missing an inclusive/exclusive endpoint.