Question

solve for r and graph the solution. |56 - 7r| > 21 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 the absolute - value inequality

The absolute - value inequality \(|56 - 7r|>21\) can be rewritten as two separate inequalities: \(56 - 7r>21\) or \(56 - 7r < - 21\).

Step2: Solve the first inequality \(56 - 7r>21\)

Subtract 56 from both sides: \(-7r>21 - 56\), so \(-7r>-35\). Divide both sides by - 7. When dividing an inequality by a negative number, the direction of the inequality sign changes. We get \(r < 5\).

Step3: Solve the second inequality \(56 - 7r < - 21\)

Subtract 56 from both sides: \(-7r<-21 - 56\), so \(-7r<-77\). Divide both sides by - 7. Since we are dividing by a negative number, the inequality sign changes, and we get \(r>11\).

Answer:

The solution is \(r < 5\) or \(r>11\). On the number - line, we have an open circle at \(r = 5\) and an arrow pointing to the left for \(r < 5\), and an open circle at \(r = 11\) and an arrow pointing to the right for \(r>11\).