Question

graph the solution to the inequality on the number line. |5u - 10| < 5

Explanation:

Step1: Rewrite absolute - value inequality

If \(|5u - 10|\lt5\), then \(- 5\lt5u - 10\lt5\).

Step2: Solve the left - hand side of the compound inequality

Add 10 to all parts: \(-5 + 10\lt5u-10 + 10\lt5 + 10\), which simplifies to \(5\lt5u\lt15\).

Step3: Solve for \(u\)

Divide all parts by 5: \(\frac{5}{5}\lt\frac{5u}{5}\lt\frac{15}{5}\), so \(1\lt u\lt3\).

Step4: Graph on number line

On the number line, draw an open circle at \(u = 1\) and an open circle at \(u = 3\), and shade the region between them.

Answer:

On the given number line, draw open circles at 1 and 3 and shade the region between 1 and 3.