1. **State the problem:** Solve the equation $5(4 - x) = 7 - 3x$ for $x$. 2. **Use the distributive property:** Multiply $5$ by each term inside the parentheses: $$5 \times 4 - 5 \times x = 20 - 5x$$ So the equation becomes: $$20 - 5x = 7 - 3x$$ 3. **Isolate variable terms on one side:** Add $5x$ to both sides to move variable terms to the right: $$20 = 7 - 3x + 5x$$ Simplify the right side: $$20 = 7 + 2x$$ 4. **Isolate the variable term:** Subtract $7$ from both sides: $$20 - 7 = 2x$$ $$13 = 2x$$ 5. **Solve for $x$:** Divide both sides by $2$: $$x = \frac{13}{2}$$ **Final answer:** $$x = \frac{13}{2}$$