Given the conditions |x|>2 and |x-4|>2, which of the following values is included in the range of x?

Answer Choices

Correct answer marked below

-1.5

3.5

Correct

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Official Explanation

Official

To determine the range of x, we analyze the inequalities. The condition |x|>2 implies that x must be either less than -2 or greater than 2, which can be expressed as x < -2 or x > 2. The second condition |x-4|>2 means that x must be more…

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Comments

pitrujaFeb 19, 2024

thanks for posting

What this question tests

What it tests

Your ability to solve absolute-value equations and inequalities by considering both cases.

Common trap

Dropping the absolute value bars entirely or missing that |x| = k has two solutions when k > 0.