First, solve the equation |2x| - 3x = 32

If x is negative, then the equation becomes -2x - 3x = 32, which simplifies to -5x = 32. Solving for x, we get x = -32/5.

If x is positive, the equation becomes 2x - 3x = 32, which simplifies to -x = 32. Solving for x, we get x = -32.

Next, solve the equation |7-x| = |2x-5|

If x is negative, the equation becomes |7 + x| = |2x - 5|. Substituting x = -32/5, we get |7 - (-32/5)| = |-69/5 + 5| which simplifies to |-119/5| = |-44/5|. Since |-119/5| is not equal to |-44/5|, x = -32/5 is not a solution.

If x is positive, the equation becomes |7 - x| = |2x - 5|. Substituting x = -32, we get |7 - (-32)| = |2(-32) - 5| which simplifies to |39| = |-69|. Since |39| is not equal to |-69|, x = -32 is not a solution.

Therefore, there are no real solutions to the equation |7-x| = |2x-5|.