Question

solve for c and graph the solution.
5 ≥ |10 - 5c|
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: Rewrite absolute - value inequality

The inequality $5\geq|10 - 5c|$ is equivalent to $- 5\leq10 - 5c\leq5$.

Step2: Solve the left - hand side of the compound inequality

Solve $-5\leq10 - 5c$. Subtract 10 from both sides: $-5-10\leq10 - 5c-10$, which simplifies to $-15\leq - 5c$. Divide both sides by - 5 and reverse the inequality sign (since dividing by a negative number), we get $3\geq c$ or $c\leq3$.

Step3: Solve the right - hand side of the compound inequality

Solve $10 - 5c\leq5$. Subtract 10 from both sides: $10 - 5c-10\leq5 - 10$, which simplifies to $-5c\leq - 5$. Divide both sides by - 5 and reverse the inequality sign, we get $c\geq1$.

Answer:

The solution is $1\leq c\leq3$. On the number line, click on the points at $c = 1$ and $c = 3$ and make them filled - in circles, then click between them to graph the line segment.