Question

|4x + 8| < 17
step 2 of 2: determine which graph represents the original inequality.

Explanation:

Step1: Solve the absolute - value inequality

For \(|a|\lt b\) (\(b\gt0\)), it is equivalent to \(-b\lt a\lt b\).
Here \(a = 4x + 8\) and \(b = 17\), so \(-17\lt4x + 8\lt17\).
Subtract 8 from all parts of the compound inequality:
\(-17-8\lt4x+8 - 8\lt17 - 8\), which simplifies to \(-25\lt4x\lt9\).
Divide all parts by 4: \(\frac{-25}{4}\lt x\lt\frac{9}{4}\), or \(-6.25\lt x\lt2.25\).

Step2: Analyze the graph

The graph of the solution \(-6.25\lt x\lt2.25\) is a number - line with open circles at \(x=-6.25\) and \(x = 2.25\) and a line segment connecting them.

Answer:

The graph with open circles at \(x=-6.25\) and \(x = 2.25\) and a line segment between them.