Question

what does {x | x > -2 and x ≤ 5} represent?
all numbers less than -2 and greater than 5
all numbers less than -2 and greater than or equal to 5
all numbers greater than or equal to -2 and less than or equal to 5
all numbers greater than -2 and less than or equal to 5

Explanation:

Step1: Analyze set - builder notation

The set $\{x|x > - 2\text{ and }x\leq5\}$ means we are looking for values of $x$. The first condition $x > - 2$ indicates values larger than -2. The second condition $x\leq5$ indicates values less than or equal to 5. So it represents all numbers that satisfy both conditions simultaneously. That is all numbers greater than -2 and less than or equal to 5.

Answer:

D. all numbers greater than -2 and less than or equal to 5