### Instruction: Solve  \[\frac{3x+2}{x-1}=4\]for $x$.### Response: This problem involves fractions and equations, so I want to simplify it as much as possible.
One way to do that is to multiply both sides of the equation by the denominator of the fraction, which is $x-1$.
This will clear the fraction and leave me with a linear equation.
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 \[x=6.\]