1. **Problem statement:** Given the binary operation $x * y = 5y - 3x$, find the value of $3 * 2$. 2. **Formula used:** The operation is defined as $x * y = 5y - 3x$. 3. **Step-by-step solution:** 1. Substitute $x = 3$ and $y = 2$ into the formula: $$3 * 2 = 5(2) - 3(3)$$ 2. Calculate each term: $$5(2) = 10$$ $$3(3) = 9$$ 3. Substitute back: $$3 * 2 = 10 - 9$$ 4. Simplify: $$3 * 2 = 1$$ 4. **Answer:** The value of $3 * 2$ is $1$. This completes the solution for the first question.