1) To solve |2x+1| = 7, we need to consider two cases: when 2x+1 is positive and when it is negative.

Case 1: 2x+1 is positive
2x+1 = 7
2x = 6
x = 3

Case 2: 2x+1 is negative
-(2x+1) = 7
-2x-1 = 7
-2x = 8
x = -4

Therefore, the solutions are x = 3 and x = -4.

2) To solve |-4x+3| = 0, we need to consider two cases:

Case 1: -4x+3 is positive
-4x+3 = 0
-4x = -3
x = 3/4

Case 2: -4x+3 is negative
-(-4x+3) = 0
4x-3 = 0
4x = 3
x = 3/4

Therefore, the solution is x = 3/4.

3) To solve |5x-7| = -3x, we consider two cases:

Case 1: 5x-7 is positive
5x-7 = -3x
8x = 7
x = 7/8

Case 2: 5x-7 is negative
-(5x-7) = -3x
-5x+7 = -3x
-2x = -7
x = 7/2

Therefore, the solutions are x = 7/8 and x = 7/2.