Question

which graph represents the solution set of the compound inequality - 5 < a - 15 < 2

Explanation:

Step1: Solve the left - hand side inequality

Add 15 to both sides of $-5 < a - 15$. We get $-5+15 < a-15 + 15$, which simplifies to $10 < a$.

Step2: Solve the right - hand side inequality

Add 15 to both sides of $a - 15 < 2$. We get $a-15 + 15<2 + 15$, which simplifies to $a < 17$.

Step3: Analyze the solution on the number line

The solution of the compound inequality is $10 < a < 17$. On a number line, this is represented by an open - circle at 10 (since 10 is not included) and an open - circle at 17 (since 17 is not included), with the line segment between them shaded.

Answer:

The number line with an open - circle at 10, an open - circle at 17, and the line segment between them shaded.