Question

solve for c and graph the solution. |c - 760| > 30 click two endpoints to graph a line segment, an endpoin ray, or two arrowheads to graph a line. to change endpoints circles, click on them. 730 740 750 760 770 780 790 800 810

Explanation:

Step1: Recall absolute value inequality rule

For \(|x| > a\) (where \(a>0\)), the solution is \(x < -a\) or \(x > a\). Applying this to \(|c - 760| > 30\), we get two inequalities:
\(c - 760 < - 30\) or \(c - 760 > 30\)

Step2: Solve the first inequality

Solve \(c - 760 < - 30\). Add 760 to both sides:
\(c < - 30 + 760\)
\(c < 730\)

Step3: Solve the second inequality

Solve \(c - 760 > 30\). Add 760 to both sides:
\(c > 30 + 760\)
\(c > 790\)

Answer:

The solution for \(c\) is \(c < 730\) or \(c > 790\). To graph this, we draw an open circle at 730 and an arrow to the left, and an open circle at 790 and an arrow to the right on the number line.