1. **State the problem:** Solve the equation $$\frac{7x - 2}{4} = 3x + 1$$ for $x$. 2. **Formula and rules:** To solve for $x$, we want to isolate $x$ on one side. Since $x$ is inside a fraction, first eliminate the denominator by multiplying both sides by 4. 3. **Multiply both sides by 4:** $$4 \times \frac{7x - 2}{4} = 4 \times (3x + 1)$$ This simplifies to: $$7x - 2 = 4(3x + 1)$$ 4. **Distribute 4 on the right side:** $$7x - 2 = 12x + 4$$ 5. **Bring all $x$ terms to one side and constants to the other:** Subtract $12x$ from both sides: $$7x - 12x - 2 = 12x - 12x + 4$$ $$-5x - 2 = 4$$ 6. **Add 2 to both sides:** $$-5x - 2 + 2 = 4 + 2$$ $$-5x = 6$$ 7. **Divide both sides by $-5$ to solve for $x$:** $$x = \frac{6}{-5}$$ 8. **Simplify the fraction:** $$x = -\frac{6}{5}$$ **Final answer:** $$x = -\frac{6}{5}$$