Determine the solution set for the inequality $(2+|x|)(2+x) > 0$ .

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x > -2

Correct

x < -2

x < 0

x > 0

x > 2

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Official Explanation

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To find the solution set of (2+|x|)(2+x) > 0, let a = (2+|x|)(2+x). Since a > 0, it follows that (2+|x|) must be positive and (2+x) must also be positive, or both (2+|x|)…

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Comments

ShehranJul 25, 2024

greatt question!

AnuragApr 9, 2024

Great!

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.

Determine the solution set for the inequality (2+∣x∣)(2+x)>0(2+|x|)(2+x) > 0(2+∣x∣)(2+x)>0.