Given that |x - 2| > 3, which of the following statements must hold true?
(I) $|x|>5$
(II) $x^{2} >16$
(III) $x>5$

Correct answer marked below

I only

II only

I and II only

II and III only

None of the above

Correct

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Official Explanation

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Starting with the inequality |x - 2| > 3, we can break it down into two cases: x - 2 > 3 or x - 2 < -3. This leads to x >…

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What this question tests

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

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