2. \( \frac{x-1}{2}-\frac{x-2}{3}-\frac{x-3}{4}=5 \)

To solve the equation \( \frac{x-1}{2}-\frac{x-2}{3}-\frac{x-3}{4}=5 \), we first find a common denominator, which in this case is 12. Rewriting the equation with this common denominator gives us: \[ 6(x - 1) - 4(x - 2) - 3(x - 3) = 60 \] Distributing gives: \[ 6x - 6 - 4x + 8 - 3x + 9 = 60 \] Combining like terms, we have: \[ (6x - 4x - 3x) + (-6 + 8 + 9) = 60 \] \[ -x + 11 = 60 \] Now, to isolate \( x \), we subtract 11 from both sides: \[ -x = 49 \] Multiplying by -1 gives: \[ x = -49 \] So, the solution to the equation is \( x = -49 \).