Solve for $x$: $\frac{3x - 1}{4x-4} = \frac23$.
To solve for $x$, I want to isolate it on one side of the equation by using inverse operations. First, I can cross-multiply to get rid of the fractions: $(3x-1)(3) = (4x-4)(2)$. Then, I can expand the brackets by applying the distributive property: $9x - 3 = 8x - 8$. Next, I can subtract $8x$ from both sides to collect the $x$ terms on the left: $9x - 8x - 3 = 8x - 8x - 8$, which simplifies to $x - 3 = -8$. Finally, I can add $3$ to both sides to get $x$ by itself: $x - 3 + 3 = -8 + 3$, which simplifies to $x = -5$. Therefore, $x = -5$ is the correct solution.

