which graph represents the solution set of the compound inequality? -5 < a - 4 < 2

Explanation:

Step1: Isolate the variable a

Add 4 to all parts of the inequality $-5 < a - 4 < 2$. We get $-5+4 < a-4 + 4<2 + 4$, which simplifies to $-1 < a<6$.

Step2: Analyze the graph

The solution set $-1 < a<6$ represents all real - numbers a such that a is greater than - 1 and less than 6. On a number line, this is represented by an open circle at - 1, an open circle at 6, and a line segment connecting them.

Answer:

The graph with an open circle at - 1, an open circle at 6, and a line segment between them.