Question

1. $-8 leq \frac{x}{-3} - 9$

Explanation:

Step1: Add 9 to both sides

To isolate the term with \( x \), we add 9 to both sides of the inequality \(-8 \leq \frac{x}{-3} - 9\). This gives us \(-8 + 9 \leq \frac{x}{-3} - 9 + 9\), which simplifies to \(1 \leq \frac{x}{-3}\).

Step2: Multiply both sides by -3 (and reverse inequality)

When we multiply or divide an inequality by a negative number, we must reverse the inequality sign. So, we multiply both sides of \(1 \leq \frac{x}{-3}\) by -3. This gives us \(1 \times (-3) \geq \frac{x}{-3} \times (-3)\) (note the reversed inequality), which simplifies to \(-3 \geq x\) or \(x \leq -3\).

Answer:

\(x \leq -3\)