Solve \( \frac{x-1}{3}-\frac{x+2}{4}=2 \) Your Answer:

To solve the equation \( \frac{x-1}{3}-\frac{x+2}{4}=2 \), we can start by finding a common denominator for the fractions, which is 12. Rewriting the equation, we get: \[ \frac{4(x-1)}{12} - \frac{3(x+2)}{12} = 2 \] Now, multiplying through by 12 gives: \[ 4(x-1) - 3(x+2) = 24 \] Expanding both sides results in: \[ 4x - 4 - 3x - 6 = 24 \] Combining like terms leads to: \[ x - 10 = 24 \] Adding 10 to both sides yields: \[ x = 34 \] So, the solution to the equation \( \frac{x-1}{3} - \frac{x+2}{4} = 2 \) is \( x = 34 \). To check, substituting \( x = 34 \) back into the original equation gives: \[ \frac{34-1}{3} - \frac{34+2}{4} = \frac{33}{3} - \frac{36}{4} = 11 - 9 = 2 \] Thus, the solution is verified: \( x = 34 \).