1. **State the problem:** Solve the equation $3(x - 5) = 2(x + 1) + 4$ for $x$. 2. **Use the distributive property:** Expand both sides: $$3(x - 5) = 3x - 15$$ $$2(x + 1) = 2x + 2$$ So the equation becomes: $$3x - 15 = 2x + 2 + 4$$ 3. **Simplify the right side:** $$2x + 2 + 4 = 2x + 6$$ So the equation is: $$3x - 15 = 2x + 6$$ 4. **Isolate variable terms on one side:** Subtract $2x$ from both sides: $$3x - 15 - 2x = 2x + 6 - 2x$$ $$\cancel{3x} - 15 - \cancel{2x} = \cancel{2x} + 6 - \cancel{2x}$$ $$x - 15 = 6$$ 5. **Isolate $x$:** Add 15 to both sides: $$x - 15 + 15 = 6 + 15$$ $$x + \cancel{-15} + \cancel{15} = 21$$ $$x = 21$$ **Final answer:** $x = 21$