1. **State the problem:** Solve the inequality $$15 - \frac{7x}{5} \geq 9$$ for $$x$$. 2. **Isolate the term with $$x$$:** Subtract 15 from both sides: $$15 - \frac{7x}{5} - 15 \geq 9 - 15$$ which simplifies to $$- \frac{7x}{5} \geq -6$$ 3. **Multiply both sides by -5 to clear the denominator and the negative sign:** Remember, multiplying by a negative number reverses the inequality sign. $$\cancel{-5} \times \left(- \frac{7x}{\cancel{5}}\right) \leq \cancel{-5} \times (-6)$$ which simplifies to $$7x \leq 30$$ 4. **Divide both sides by 7 to solve for $$x$$:** $$x \leq \frac{30}{7}$$ 5. **Interpret the solution:** The solution set is all $$x$$ such that $$x \leq \frac{30}{7}$$. 6. **Check the graph description:** The graph shows shading to the right of a certain value, indicating $$x \geq$$ something. Our solution is $$x \leq \frac{30}{7}$$, which is shading to the left. **Final answer:** $$x \leq \frac{30}{7}$$