Question

graph the solution to the inequality on the number line. |9 - 6u| < 15

Explanation:

Step1: Rewrite the absolute - value inequality

An absolute - value inequality \(|a|\lt b\) (\(b > 0\)) is equivalent to \(-b\lt a\lt b\). So, \(|9 - 6u|\lt15\) is equivalent to \(-15\lt9 - 6u\lt15\).

Step2: Subtract 9 from all parts of the compound inequality

\(-15-9\lt9 - 6u-9\lt15 - 9\), which simplifies to \(-24\lt - 6u\lt6\).

Step3: Divide all parts by - 6 and reverse the inequality signs

When dividing an inequality by a negative number, the direction of the inequality signs changes. So, \(\frac{-24}{-6}>\frac{-6u}{-6}>\frac{6}{-6}\), which gives \(4 > u>-1\) or \(-1\lt u\lt4\).

Step4: Graph on the number line

On the number line, we draw an open circle at \(u=-1\) and an open circle at \(u = 4\), and then shade the region between them.

Answer:

On the number line, draw open circles at \(u=-1\) and \(u = 4\), and shade the region between them.