The triangle inequality theorem states that the sum of two sides of a triangle must be longer than the thrid side. Therefore:
x+4 + x + 5 > 4x -3
12 > 4x - 2x
12>2x
6>x 6
x+4 +4x - 3 > x+5
5x -x > 5-4+3
4x>4
x> 1
x+5+4x-3 > x+4
4x > 4 - 5 +3
4x> 2
x> 1/2 x>1/3 is false