You can first expand the left side, from -4(x+4) to -4x-16
On the other side of the inequality, you can combine like terms, x+7-2x+3 = x-2x+7+3 = -x+10.
The simpolifies inequality is now -4x-16 > -x+10
Adding 4x to both sides, -16 > 3x+10
Subtracting 10 from both sides, -26 > 3x
Dividing 3 from both sides, -26/3 > x
Switching the inequality, we get x < -26/3