Question

graph the solution to the inequality on the number line. |w + 3| < 7

Explanation:

Step1: Rewrite absolute - value inequality

If \(|a|\lt b\) (\(b > 0\)), then \(-b\lt a\lt b\). So for \(|w + 3|\lt7\), we have \(-7\lt w+3\lt7\).

Step2: Solve the compound inequality

Subtract 3 from all parts: \(-7-3\lt w + 3-3\lt7 - 3\), which simplifies to \(-10\lt w\lt4\).

Step3: Graph on number - line

On the number - line, we draw an open circle at \(w=-10\) and \(w = 4\) (because the inequality is strict, i.e., \(\lt\) not \(\leq\)) and shade the region between them.

Answer:

On the number - line, draw open circles at \(-10\) and \(4\) and shade the region between them.