Question

solve for c and graph the solution.
|c + 3| > 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.
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3
submit

Explanation:

Step1: Recall absolute value inequality rule

For \(|x|>a\) (where \(a > 0\)), the solution is \(x > a\) or \(x < -a\). So for \(|c + 3|>4\), we have two cases.

Step2: Solve the first inequality \(c + 3>4\)

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

Step3: Solve the second inequality \(c + 3<-4\)

Subtract 3 from both sides: \(c+3 - 3<-4 - 3\), which simplifies to \(c < - 7\).

Answer:

The solution for \(c\) is \(c < - 7\) or \(c > 1\). To graph this, we have two rays: one with an empty circle at \(-7\) and an arrow pointing to the left (for \(c < - 7\)), and one with an empty circle at \(1\) and an arrow pointing to the right (for \(c > 1\)).