Question

solve for z and graph the solution. |8z - 625| < 200. click two endpoints to graph a line segment, an endpoint and an arrowhead to graph a ray, or two arrowheads to graph a line. to change endpoints from filled - in circles to empty circles, click on them.

Explanation:

Step1: Rewrite the absolute - value inequality

The absolute - value inequality \(|8z - 625|\lt200\) can be rewritten as \(- 200\lt8z - 625\lt200\).

Step2: Add 625 to all parts of the compound inequality

Adding 625 to each part gives \(-200 + 625\lt8z-625 + 625\lt200 + 625\), which simplifies to \(425\lt8z\lt825\).

Step3: Divide all parts by 8

Dividing each part by 8, we get \(\frac{425}{8}\lt z\lt\frac{825}{8}\), or \(53.125\lt z\lt103.125\).

Answer:

The solution of the inequality is \(53.125\lt z\lt103.125\). On the number - line, we mark an open circle at \(z = 53.125\) and an open circle at \(z = 103.125\) and draw a line segment between them.