1. **Problem:** Solve the equation $3(5x - 1) = 4(3x + 2)$. 2. **Formula and rules:** Use the distributive property $a(b+c) = ab + ac$ to expand both sides. 3. **Step-by-step solution:** - Expand both sides: $$3(5x - 1) = 15x - 3$$ $$4(3x + 2) = 12x + 8$$ - Set the equation: $$15x - 3 = 12x + 8$$ - Subtract $12x$ from both sides: $$15x - 12x - 3 = 8$$ $$3x - 3 = 8$$ - Add 3 to both sides: $$3x = 11$$ - Divide both sides by 3: $$x = \frac{11}{3}$$ 4. **Answer:** $$x = \frac{11}{3}$$