Which of the following inequalities represents the entire solution set for x if |x| > x?

BTGmoderatorDC wrote: ↑

Fri Oct 08, 2021 6:26 pm

Which of the following inequalities represents the entire solution set for x if |x| > x?

A. x ≥ 0
B. x > 0
C. x ≤ 0
D. x < 0
E. x < −1


OA D

Source: Veritas Prep

One approach is to test numbers...

For example, does x = 1 satisfy the given inequality?
When we test, we get |1| > 1, which is not true.
Since x = 1 is NOT a solution, we can eliminate answer choices A and B, because they say that x = 1 IS a solution.

Now let's test another number.
Does x = 0 satisfy the given inequality?
When we test, we get |0| > 0, which is not true.
Since x = 1 is NOT a solution, we can eliminate answer choice C, because it says that x = 0 IS a solution.

We are down to D or E.
Does x = -1 satisfy the given inequality?
When we test, we get |-1| > -1, which is true.
Since x = -1 IS a solution, we can eliminate answer choice E, because is says that x = 0 is NOT a solution.

By the process of elimination, the correct answer is D.