Question

solve for c and graph the solution. 8 > |c - 7| + 7 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: Isolate the absolute - value expression

Subtract 7 from both sides of the inequality $8>\vert c - 7\vert+7$.
$8-7>\vert c - 7\vert+7 - 7$
$1>\vert c - 7\vert$ or $\vert c - 7\vert<1$.

Step2: Rewrite the absolute - value inequality as a compound inequality

If $\vert x\vert < a$ ($a>0$), then $-a < x < a$. Here $x = c - 7$ and $a = 1$.
$-1 < c - 7 < 1$.

Step3: Solve the compound inequality for c

Add 7 to all parts of the compound inequality.
$-1+7 < c - 7+7 < 1+7$
$6 < c < 8$.

Answer:

The solution of the inequality is $6 < c < 8$. To graph it, click on the number 6 and 8 on the number - line and change the endpoints to empty circles.