### Instruction: Simplify $\frac{x+1}{3}+\frac{2-3x}{2}$.  Express your answer as a single fraction.### Response: To add two fractions, I need to have a common denominator.
So I will look for the least common multiple of 3 and 2, which is 6.
To get a denominator of 6 for the first fraction, I need to multiply both the numerator and denominator by 2.
That gives me $\frac{2x+2}{6}$.
To get a denominator of 6 for the second fraction, I need to multiply both the numerator and denominator by 3.
That gives me $\frac{6-9x}{6}$.
Now I can add the fractions by adding the numerators and keeping the same denominator.
That gives me $\frac{2x+2+6-9x}{6}$.
I can simplify the numerator by combining like terms.
I have $2x-9x=-7x$ and $2+6=8$.
So the numerator becomes $-7x+8$.
The fraction is now $\frac{-7x+8}{6}$, and I cannot simplify it further.