2(4x-2)+3(x-7)=6(5x+4)-11(x+3)

To solve the equation \( 2(4x - 2) + 3(x - 7) = 6(5x + 4) - 11(x + 3) \), we will first expand and simplify both sides.

1. Expand both sides:

   • Left Side: \[ 2(4x - 2) = 8x - 4 \] \[ 3(x - 7) = 3x - 21 \] Therefore, the left side becomes: \[ 8x - 4 + 3x - 21 = 11x - 25 \]

   • Right Side: \[ 6(5x + 4) = 30x + 24 \] \[ -11(x + 3) = -11x - 33 \] Therefore, the right side becomes: \[ 30x + 24 - 11x - 33 = 19x - 9 \]

2. Now we have the equation: \[ 11x - 25 = 19x - 9 \]

3. Rearranging the terms to isolate \(x\): \[ 11x - 19x = -9 + 25 \] \[ -8x = 16 \] \[ x = \frac{16}{-8} = -2 \]

4. The solution is: \[ x = -2 \]

If needed, you can substitute \(x = -2\) back into the original equation to verify the solution is correct.