Question

graph the solution to the inequality on the number line. |x - 3| < 6

Explanation:

Step1: Remove absolute - value

If \(|a|\lt b\) (\(b > 0\)), then \(-b\lt a\lt b\). So for \(|x - 3|\lt6\), we have \(-6\lt x - 3\lt6\).

Step2: Solve the compound - inequality

Add 3 to all parts of the compound - inequality: \(-6+3\lt x-3 + 3\lt6 + 3\), which simplifies to \(-3\lt x\lt9\).

Step3: Graph on number line

On the number line, we use open circles at \(x=-3\) and \(x = 9\) (because the inequality is strict, i.e., \(\lt\) not \(\leq\)) and shade the region between them.

Answer:

On the number line, place open circles at \(-3\) and \(9\) and shade the region between them.