Solve  \[\frac{3x+2}{x-1}=4\]for $x$.
One way to do that is to multiply both sides of the equation by the denominator of the fraction, which is $x-1$. So I multiply both sides by $x-1$ and get \[3x+2=4(x-1).\] Now I need to solve for $x$ by using the distributive property, combining like terms, and isolating $x$ on one side. First, I distribute the 4 on the right side and get \[3x+2=4x-4.\] Then, I subtract $4x$ from both sides to eliminate it from the right side and get \[-x+2=-4.\] Next, I subtract $2$ from both sides to eliminate it from the left side and get \[-x=-6.\] Finally, I divide both sides by $-1$ to get $x$ by itself and get \[x=6.\] 