4x+3>2(3x-4)-2x

Solve the inequality:

4x + 3 > 2(3x - 4) - 2x

Compute the right side: 2(3x - 4) = 6x - 8, so 6x - 8 - 2x = 4x - 8.

Thus: 4x + 3 > 4x - 8

Subtract 4x from both sides: 3 > -8, which is true.

Therefore the inequality holds for all real x. Solution: all real numbers ((-∞, ∞)).