Question: Solve the equation for x
9 (x + 1) + 2 = -4 (x - 9) - 4
x =
1. **State the problem:** Solve the equation $$9 (x + 1) + 2 = -4 (x - 9) - 4$$ for $$x$$.
2. **Apply the distributive property:**
$$9(x + 1) = 9x + 9$$
$$-4(x - 9) = -4x + 36$$
So the equation becomes:
$$9x + 9 + 2 = -4x + 36 - 4$$
3. **Simplify both sides:**
$$9x + 11 = -4x + 32$$
4. **Add $$4x$$ to both sides to get all $$x$$ terms on one side:**
$$9x + 4x + 11 = -4x + 4x + 32$$
$$13x + 11 = 32$$
5. **Subtract 11 from both sides:**
$$13x + \cancel{11} - \cancel{11} = 32 - 11$$
$$13x = 21$$
6. **Divide both sides by 13 to solve for $$x$$:**
$$x = \frac{21}{13}$$
**Final answer:**
$$x = \frac{21}{13}$$