1. The problem asks to solve the equation $$\frac{3x+1}{x-2} = 2$$ for $x$. 2. The formula used here is to solve rational equations by eliminating the denominator: multiply both sides by the denominator to clear the fraction. 3. Multiply both sides by $x-2$: $$\cancel{\frac{3x+1}{x-2}} \times (x-2) = 2 \times (x-2)$$ which simplifies to $$3x + 1 = 2(x - 2)$$ 4. Expand the right side: $$3x + 1 = 2x - 4$$ 5. Subtract $2x$ from both sides: $$3x - \cancel{2x} + 1 = \cancel{2x} - 4$$ which simplifies to $$x + 1 = -4$$ 6. Subtract 1 from both sides: $$x + \cancel{1} - \cancel{1} = -4 - 1$$ which simplifies to $$x = -5$$ 7. Check the solution by substituting $x = -5$ back into the original equation: $$\frac{3(-5) + 1}{-5 - 2} = \frac{-15 + 1}{-7} = \frac{-14}{-7} = 2$$ which is true. Therefore, the solution is $$x = -5$$.