1. **State the problem:** Solve for $x$ in the equation $3(x+9)-(15-x)=8(x+1)$. 2. **Apply the distributive property:** $$3(x+9) = 3x + 27$$ $$-(15-x) = -15 + x$$ So the equation becomes: $$3x + 27 - 15 + x = 8(x+1)$$ 3. **Simplify the left side:** $$3x + x + 27 - 15 = 4x + 12$$ 4. **Rewrite the equation:** $$4x + 12 = 8(x+1)$$ 5. **Distribute on the right side:** $$8(x+1) = 8x + 8$$ 6. **Rewrite the equation:** $$4x + 12 = 8x + 8$$ 7. **Bring all terms involving $x$ to one side and constants to the other:** $$4x + 12 - 8x = 8$$ $$\cancel{4x} + 12 - \cancel{8x} = 8$$ $$-4x + 12 = 8$$ 8. **Subtract 12 from both sides:** $$-4x + 12 - 12 = 8 - 12$$ $$-4x = -4$$ 9. **Divide both sides by $-4$ to solve for $x$:** $$x = \frac{-4}{-4}$$ $$x = 1$$ **Final answer:** $$x = 1$$