Question

solve for q and graph the solution.
|9q + 54| > 45
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: Solve the inequality \(|9q + 54|>45\)

We know that if \(|x|>a\) (\(a>0\)), then \(x > a\) or \(x<-a\).
For \(|9q + 54|>45\), we have two cases:
Case 1: \(9q+54>45\)
Subtract 54 from both sides: \(9q>45 - 54\)
\(9q>-9\)
Divide both sides by 9: \(q>- 1\)
Case 2: \(9q + 54<-45\)
Subtract 54 from both sides: \(9q<-45-54\)
\(9q<-99\)
Divide both sides by 9: \(q<-11\)

Answer:

The solution of the inequality \(|9q + 54|>45\) is \(q < - 11\) or \(q>-1\). On the number - line, we graph a ray starting at \(-11\) (with an empty circle) and going to the left, and a ray starting at \(-1\) (with an empty circle) and going to the right.