Question: Solve for x and simplify the answer fully.
$$\frac{3x + 4}{7} = \frac{1}{3}$$
1. **State the problem:** Solve for $x$ in the equation $$\frac{3x + 4}{7} = \frac{1}{3}$$.
2. **Use the cross-multiplication formula:** When two fractions are equal, their cross products are equal:
$$ (3x + 4) \times 3 = 7 \times 1 $$
3. **Multiply both sides:**
$$ 3(3x + 4) = 7 $$
4. **Distribute the 3:**
$$ 9x + 12 = 7 $$
5. **Isolate the term with $x$ by subtracting 12 from both sides:**
$$ 9x + 12 - 12 = 7 - 12 $$
$$ 9x = -5 $$
6. **Divide both sides by 9 to solve for $x$:**
$$ x = \frac{-5}{9} $$
7. **Simplify if possible:** The fraction $\frac{-5}{9}$ is already in simplest form.
**Final answer:**
$$ x = -\frac{5}{9} $$