Question: Solve for $x$. Express your answer as a whole number, a decimal, or a fraction in simplest form.
$-10x + 3(3x + 4) + 1 = -3(7x + 3)$
1. **State the problem:** Solve the equation $$-10x + 3(3x + 4) + 1 = -3(7x + 3)$$ for $x$.
2. **Apply the distributive property:**
$$-10x + 3 \times 3x + 3 \times 4 + 1 = -3 \times 7x - 3 \times 3$$
which simplifies to
$$-10x + 9x + 12 + 1 = -21x - 9$$
3. **Combine like terms on the left side:**
$$(-10x + 9x) + (12 + 1) = -21x - 9$$
$$-x + 13 = -21x - 9$$
4. **Add $21x$ to both sides to get all $x$ terms on one side:**
$$-x + 21x + 13 = -21x + 21x - 9$$
$$20x + 13 = -9$$
5. **Subtract 13 from both sides:**
$$20x + 13 - 13 = -9 - 13$$
$$20x = -22$$
6. **Divide both sides by 20 to solve for $x$:**
$$x = \frac{-22}{20}$$
7. **Simplify the fraction by dividing numerator and denominator by their greatest common divisor 2:**
$$x = \frac{\cancel{22}^{11}}{\cancel{20}^{10}} = -\frac{11}{10}$$
**Final answer:**
$$x = -\frac{11}{10}$$