Question

problem 2
click and drag to graph all the solutions to the inequality
|x + 2| > 4.

Explanation:

Step1: Solve the absolute - value inequality

For the inequality \(|x + 2|>4\), we use the property that if \(|u|>a\) (\(a>0\)), then \(u>a\) or \(u < - a\).
Here \(u=x + 2\) and \(a = 4\). So we have two inequalities:

1. \(x+2>4\)

Subtract 2 from both sides: \(x+2-2>4 - 2\), which gives \(x>2\).

1. \(x + 2<-4\)

Subtract 2 from both sides: \(x+2-2<-4 - 2\), which gives \(x<-6\).

Answer:

The solutions of the inequality \(|x + 2|>4\) are \(x>2\) or \(x<-6\). On the number - line, we have an open circle at \(x = 2\) (since \(x\) is not equal to 2) and the line extends to the right of 2, and an open circle at \(x=-6\) (since \(x\) is not equal to - 6) and the line extends to the left of - 6.