Question

solve for u and graph the solution.
|u + 60| > 40
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 absolute - value inequality

For the inequality \(|u + 60|>40\), we use the property that if \(|x|>a\) (\(a>0\)), then \(x>a\) or \(x < - a\).
Here, \(x = u + 60\) and \(a = 40\). So we have two cases:
Case 1: \(u+60>40\)
Subtract 60 from both sides: \(u+60 - 60>40 - 60\), which simplifies to \(u>-20\).
Case 2: \(u + 60<-40\)
Subtract 60 from both sides: \(u+60-60<-40 - 60\), which simplifies to \(u<-100\).

Step2: Graph the solution

The solution of the inequality \(|u + 60|>40\) is \(u<-100\) or \(u>-20\).
On the number - line:

• For \(u < - 100\), we draw a ray starting from an open circle at \(u=-100\) and going to the left (towards more negative numbers).
• For \(u>-20\), we draw a ray starting from an open circle at \(u = - 20\) and going to the right (towards more positive numbers).

Answer:

The solution of the inequality \(|u + 60|>40\) is \(u<-100\) or \(u>-20\). On the number - line, there is an open circle at \(u=-100\) with a ray extending to the left and an open circle at \(u=-20\) with a ray extending to the right.