Question

solve for c and graph the solution. 4 ≤ |c + 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: Recall absolute - value inequality rule

For \(|x|\geq a\) (\(a\geq0\)), it is equivalent to \(x\geq a\) or \(x\leq - a\). Here \(x = c + 4\) and \(a = 4\), so \(c+4\geq4\) or \(c + 4\leq-4\).

Step2: Solve \(c + 4\geq4\)

Subtract 4 from both sides: \(c+4 - 4\geq4 - 4\), which gives \(c\geq0\).

Step3: Solve \(c + 4\leq-4\)

Subtract 4 from both sides: \(c+4 - 4\leq-4 - 4\), which gives \(c\leq-8\).

Answer:

The solution set is \(c\leq - 8\) or \(c\geq0\). On the number - line, we mark a closed circle at \(c=-8\) and draw a ray to the left, and mark a closed circle at \(c = 0\) and draw a ray to the right.