Question

solve for s.
8s + 7(-6s + 7) ≤ 7(-3s - 6)
write your answer with s first, followed by an inequality symbol.

Explanation:

Step1: Expand both sides

First, expand \(7(-6s + 7)=-42s + 49\) and \(7(-3s - 6)=-21s-42\). The inequality becomes \(8s-42s + 49\leq -21s-42\).

Step2: Combine like - terms on the left - hand side

Combine \(8s\) and \(-42s\): \((8s-42s)+49=-34s + 49\). So the inequality is \(-34s + 49\leq -21s-42\).

Step3: Add \(34s\) to both sides

\(-34s+34s + 49\leq -21s+34s-42\), which simplifies to \(49\leq13s - 42\).

Step4: Add 42 to both sides

\(49 + 42\leq13s-42 + 42\), resulting in \(91\leq13s\).

Step5: Divide both sides by 13

\(\frac{91}{13}\leq\frac{13s}{13}\), so \(7\leq s\).

Answer:

\(s\geq7\)