Solve the inequality and give the solution set.
-$| x |

Question

Solve the inequality and give the solution set.
-$| x | < - 2$
A) $\{ - 2 \}$
B) $\{ x \mid - 2 < x < 2 \}$
C) $\mathcal { R }$
D) $\varnothing$

Quizplus · Accepted Answer

The absolute value of a number, $|x|$, is always non-negative, meaning it can be zero or positive. Therefore, it is impossible for $|x|$ to be less than a negative number, such as $-2$. This means there are no real numbers that satisfy the given inequality, making the solution set empty, denoted by $\varnothing$.

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