Question

solve for c and graph the solution.
|c + 1| > 4
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: Split absolute - value inequality

We know that if \(|x|>a\) (\(a > 0\)), then \(x>a\) or \(x < - a\). For \(|c + 1|>4\), we get \(c+1>4\) or \(c + 1<-4\).

Step2: Solve \(c+1>4\)

Subtract 1 from both sides: \(c+1 - 1>4 - 1\), so \(c>3\).

Step3: Solve \(c + 1<-4\)

Subtract 1 from both sides: \(c+1-1<-4 - 1\), so \(c<-5\).

Answer:

The solution is \(c<-5\) or \(c>3\). On the number - line, we use an open circle at \(c=-5\) and draw an arrow to the left, and use an open circle at \(c = 3\) and draw an arrow to the right.