The problem asks us to find the solution to the compound inequality $5 < 3x + 17 < 71$ and identify which number line represents the solution set.

1. Problem Description

The problem asks us to find the solution to the compound inequality $5 < 3x + 17 < 71$ and identify which number line represents the solution set.

2. Solution Steps

First, we solve the inequality $5 < 3x + 17 < 71$. We can subtract 17 from all parts of the inequality:

$5 - 17 < 3x + 17 - 17 < 71 - 17$

$-12 < 3x < 54$

Next, we divide all parts of the inequality by 3:

$\frac{-12}{3} < \frac{3x}{3} < \frac{54}{3}$

$-4 < x < 18$

So the solution to the inequality is $-4 < x < 18$. This means that $x$ must be greater than $-4$ and less than

1

8. On the number line, this is represented by an open circle at -4 and an open circle at 18, with the line segment between them shaded.

3. Final Answer

The first number line shows an open circle at -4 and an open circle at 18 with the line segment between them shaded.

The solution is the first option.