Question: User: $\frac{3x+4}{7}$ = $\frac{x+8}{3}$
1. **State the problem:** Solve the equation $$\frac{3x+4}{7} = \frac{x+8}{3}$$ for $x$.
2. **Formula and rules:** To solve an equation with fractions, we can cross-multiply to eliminate the denominators. Cross-multiplying means multiplying both sides by the product of the denominators.
3. **Cross-multiply:**
$$3(3x+4) = 7(x+8)$$
4. **Expand both sides:**
$$9x + 12 = 7x + 56$$
5. **Isolate $x$ terms on one side:**
$$9x - 7x = 56 - 12$$
6. **Simplify:**
$$2x = 44$$
7. **Divide both sides by 2:**
$$x = \frac{44}{2}$$
8. **Simplify the fraction:**
$$x = \cancel{\frac{44}{2}} = 22$$
**Final answer:**
$$x = 22$$