1. **State the problem:** Solve the linear inequality $$4 - \frac{3y}{5} \leq 7$$. 2. **Isolate the term with the variable:** Subtract 4 from both sides: $$4 - \frac{3y}{5} - 4 \leq 7 - 4$$ which simplifies to $$- \frac{3y}{5} \leq 3$$. 3. **Eliminate the fraction:** Multiply both sides by 5 (positive number, so inequality direction stays the same): $$5 \times \left(- \frac{3y}{5}\right) \leq 3 \times 5$$ which simplifies to $$-3y \leq 15$$. 4. **Solve for y:** Divide both sides by -3. Since dividing by a negative number reverses the inequality: $$y \geq \frac{15}{-3}$$ which simplifies to $$y \geq -5$$. 5. **Answer:** The solution is $$y \geq -5$$, which corresponds to option B. --- **How to solve linear inequalities with mixed numbers:** - Convert mixed numbers to improper fractions first. - Then follow the same steps: isolate the variable, clear fractions by multiplying, and remember to flip the inequality sign when multiplying or dividing by a negative number. This method works for all linear inequalities, whether numbers are whole, fractions, or mixed numbers.