Solve and check x-4(x-3)+7=6-(x-4)

Solution:
1. Expand the equation:
- Left side: x - 4(x - 3) + 7 = x - 4x + 12 + 7
- Right side: 6 - (x - 4) = 6 - x + 4

2. Simplify both sides:
- Left side: x - 4x + 12 + 7 = -3x + 19
- Right side: 6 + 4 - x = 10 - x

3. Set the simplified equations equal:
-3x + 19 = 10 - x

4. Rearrange the equation to isolate terms involving x:
-3x + x = 10 - 19

5. Simplify:
-2x = -9

6. Solve for x:
x = \frac{-9}{-2} = \frac{9}{2}

7. Therefore, the solution for x is:
x = \frac{9}{2}