Question

solve for q and graph the solution. |q - 8| + 8 < 9 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: Isolate the absolute - value expression

Subtract 8 from both sides of the inequality \(|q - 8|+8\lt9\).
\(|q - 8|\lt9 - 8\), so \(|q - 8|\lt1\).

Step2: Rewrite the absolute - value inequality as a compound inequality

If \(|x|\lt a\) (\(a\gt0\)), then \(-a\lt x\lt a\). Here \(x = q - 8\) and \(a = 1\), so \(-1\lt q - 8\lt1\).

Step3: Solve the compound inequality for \(q\)

Add 8 to all parts of the compound inequality: \(-1+8\lt q - 8+8\lt1 + 8\), which simplifies to \(7\lt q\lt9\).

Step4: Graph the solution

The solution \(7\lt q\lt9\) is a line segment on the number - line with open endpoints at 7 and 9. Click on 7 and 9 and change them to open circles, then click on 7 and 9 to graph the line segment between them.

Answer:

The solution of the inequality is \(7\lt q\lt9\). The graph has open - circles at 7 and 9 and a line segment between them.