Question

graph the solution to the inequality on the number line.
|u - 5| > 3

Explanation:

Step1: Solve the inequality \(|u - 5|>3\)

Recall the rule \(|x|>a\) implies \(x>a\) or \(x < - a\).
For \(|u - 5|>3\), we have two cases:
Case 1: \(u-5>3\)
Add \(5\) to both sides: \(u-5 + 5>3+5\), so \(u>8\).
Case 2: \(u - 5<-3\)
Add \(5\) to both sides: \(u-5 + 5<-3 + 5\), so \(u<2\).

Step2: Graph the solution on the number - line

For \(u < 2\), we draw an open circle at \(u = 2\) (because \(u
eq2\)) and shade to the left.
For \(u>8\), we draw an open circle at \(u = 8\) (because \(u
eq8\)) and shade to the right.

Answer:

The solution of the inequality \(|u - 5|>3\) is \(u<2\) or \(u>8\). On the number - line, we have an open circle at \(2\) with shading to the left and an open circle at \(8\) with shading to the right.