Question

solve for q and graph the solution.
5 < |5q + 50|
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.
(then there is a number line with marks from - 19 to - 7 and a submit button on the left.)

Explanation:

Step1: Solve the absolute - value inequality

Given the inequality \( 5<|5q + 50|\). By the definition of absolute - value inequalities, if \(|x|>a\) (\(a>0\)), then \(x > a\) or \(x<-a\). Here, \(x = 5q+50\) and \(a = 5\). So we can split the inequality into two separate inequalities:

1. \(5q + 50>5\)
2. \(5q+50 < - 5\)

Step2: Solve \(5q + 50>5\)

Subtract 50 from both sides of the inequality:
\(5q+50 - 50>5 - 50\)
\(5q>-45\)
Divide both sides by 5:
\(q>\frac{-45}{5}=-9\)

Step3: Solve \(5q + 50 < - 5\)

Subtract 50 from both sides of the inequality:
\(5q+50 - 50 < - 5-50\)
\(5q < - 55\)
Divide both sides by 5:
\(q<\frac{-55}{5}=-11\)

So the solution to the inequality \(5 < |5q + 50|\) is \(q < - 11\) or \(q>-9\). To graph this solution:

• For \(q < - 11\), we draw an arrow starting from an open circle at \(q=-11\) (since the inequality is strict, \(q

eq - 11\)) and pointing to the left (towards more negative values).

• For \(q>-9\), we draw an arrow starting from an open circle at \(q = - 9\) (since the inequality is strict, \(q

eq - 9\)) and pointing to the right (towards more positive values).

Answer:

\( q < -9 \) or \( q > -11 \)