Question

solve for r and graph the solution.
$5 < |r + 35|$
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.
number line with -90, -80, -70, -60, -50, -40, -30, -20, -10, 0, 10, 20, 30

Explanation:

Step1: Recall absolute value inequality rule

For \(|x|>a\) (where \(a > 0\)), the solution is \(x > a\) or \(x < -a\). Here, \(x=r + 35\) and \(a = 5\), so we have two inequalities:
\(r+35>5\) or \(r + 35<-5\)

Step2: Solve \(r + 35>5\)

Subtract 35 from both sides:
\(r+35 - 35>5 - 35\)
\(r>- 30\)

Step3: Solve \(r + 35<-5\)

Subtract 35 from both sides:
\(r+35 - 35<-5 - 35\)
\(r<-40\)

Answer:

The solution for \(r\) is \(r < - 40\) or \(r> - 30\). To graph: For \(r < - 40\), draw an arrow to the left from an open circle at \(-40\); for \(r>-30\), draw an arrow to the right from an open circle at \(-30\).