abs(7x - 6) < 43 - 2x
do 7x - 6 < 43 - 2x and 7x - 6 > -43 + 2x
9x < 49 and 5x > -37
then x<49/9 and x>-37/5
part 2: 43 - 2x < 3 - 2x and 43 - 2x > -3 + 2x
43 - 2x < 3 - 2x is a false statement as 43 is not < 3
then 43 - 4x > -3
-4x> -47
x<47/4
when you test multiple areas less than and greater than these numbers, it does not appear that anything works.
therefore I believe the answer is no solution