Question

solve the inequality 5(6+3r)+7≥127

Explanation:

Step1: Simplify the left side.

First, distribute the 5 in \(5(6 + 3r)\): \(5\times6 + 5\times3r = 30 + 15r\). Then add 7: \(30 + 15r + 7 = 37 + 15r\). So the inequality becomes \(37 + 15r \geq 127\).

Step2: Subtract 37 from both sides.

Subtract 37 from each side: \(37 + 15r - 37 \geq 127 - 37\), which simplifies to \(15r \geq 90\).

Step3: Divide both sides by 15.

Divide both sides by 15: \(\frac{15r}{15} \geq \frac{90}{15}\), so \(r \geq 6\).

Answer:

\(r \geq 6\)