Algebra-1

The correct option is B. {x|x∈ℝ, x < 5 and x > -5}.

To determine the solution set for the inequality -|x| > -5, we can follow these steps:

Step 1: Remove the negative signs:
|x| < 5

Step 2: Solve for x:
The inequality |x| < 5 means that the absolute value of x is less than 5. This implies that x can be any real number that is within a distance of 5 units from 0.

So, the solution set is x < 5 and x > -5, which can be written as {x|x∈ℝ, x < 5 and x > -5}.

Now let's examine the other options:

A. {x|x∈ℝ, x < 5 or x > -5}: This option suggests that x can be either less than 5 or greater than -5. However, as shown above, x needs to satisfy both conditions (x < 5 and x > -5), so this option is incorrect.
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