Algebra-1

The correct option is C. {}

The solution set for the compound inequality x > -2 and -4 > x is an empty set, also represented as {}.

To understand why the other options are not correct, let's examine them:

A. {x|x∈ℝ,x > -2}: Option A represents the solution set for x > -2, but it does not take into account the second inequality, -4 > x.

B. {x|x∈ℝ,x < -4 or x > -2}: Option B represents the union of the solution set for x < -4 and x > -2. However, the two inequalities in the original problem cannot be simultaneously satisfied, so this...