Question: Solve for $x$. Express your answer as a whole number, a decimal, or a fraction in simplest form.
-5 + 2x = 5 - (-9x - 4) - 5x
1. **State the problem:** Solve the equation $$-5 + 2x = 5 - (-9x - 4) - 5x$$ for $x$.
2. **Apply the distributive property and simplify inside the parentheses:**
$$-5 + 2x = 5 - (-9x - 4) - 5x$$
The expression $-(-9x - 4)$ becomes $+9x + 4$ because the minus sign outside the parentheses changes the signs inside.
So the equation becomes:
$$-5 + 2x = 5 + 9x + 4 - 5x$$
3. **Combine like terms on the right side:**
$$5 + 4 = 9$$
$$9x - 5x = 4x$$
So the right side simplifies to:
$$9 + 4x$$
The equation is now:
$$-5 + 2x = 9 + 4x$$
4. **Get all $x$ terms on one side and constants on the other:**
Subtract $2x$ from both sides:
$$-5 + \cancel{2x} - 2x = 9 + 4x - 2x$$
$$-5 = 9 + 2x$$
Subtract $9$ from both sides:
$$-5 - 9 = 9 - 9 + 2x$$
$$-14 = 2x$$
5. **Solve for $x$ by dividing both sides by $2$:**
$$\frac{-14}{\cancel{2}} = \frac{2x}{\cancel{2}}$$
$$x = -7$$
**Final answer:**
$$x = -7$$