1. **State the problem:** Solve the equation $3y = 7 - \frac{2}{5}$ for $y$. 2. **Rewrite the equation:** The equation is $3y = 7 - \frac{2}{5}$. 3. **Find a common denominator to combine terms on the right side:** $$7 = \frac{35}{5}$$ So, $$7 - \frac{2}{5} = \frac{35}{5} - \frac{2}{5} = \frac{33}{5}$$ 4. **Substitute back:** $$3y = \frac{33}{5}$$ 5. **Divide both sides by 3 to isolate $y$:** $$y = \frac{\frac{33}{5}}{3} = \frac{33}{5} \times \frac{1}{3}$$ 6. **Simplify the multiplication:** $$y = \frac{33 \times 1}{5 \times 3} = \frac{33}{15}$$ 7. **Simplify the fraction by dividing numerator and denominator by 3:** $$y = \frac{\cancel{33}^{{11}}}{\cancel{15}^{{5}}} = \frac{11}{5}$$ **Final answer:** $$y = \frac{11}{5}$$