Question

solve the inequality and graph the solution.
5(r - 2) ≤ 10
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.
your answer:
change my answer

Explanation:

Step1: Expand the left - hand side

Use the distributive property \(a(b - c)=ab - ac\). Here \(a = 5\), \(b=r\), \(c = 2\).
\(5(r-2)=5r-10\). So the inequality becomes \(5r-10\leq10\).

Step2: Add 10 to both sides

To isolate the term with \(r\), add 10 to both sides of the inequality.
\(5r-10 + 10\leq10 + 10\), which simplifies to \(5r\leq20\).

Step3: Divide both sides by 5

Divide each side of the inequality \(5r\leq20\) by 5. Since \(5>0\), the direction of the inequality sign does not change.
\(\frac{5r}{5}\leq\frac{20}{5}\), so \(r\leq4\).

Answer:

The solution of the inequality \(5(r - 2)\leq10\) is \(r\leq4\). On the number - line, we have a closed circle at \(r = 4\) (because the inequality includes equality, i.e., \(r\) can be 4) and a ray extending to the left (towards the negative infinity).