[tex]I5x+3 I = I3-xI[/tex]

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To solve this equation, we first need to simplify the absolute values on both sides.

Given: |5x + 3| = |3 - x|

Case 1: 5x + 3 = 3 - x
Solving for x:
5x + x = 3 - 3
6x = 0
x = 0

Case 2: 5x + 3 = - (3 - x)
Solving for x:
5x + 3 = -3 + x
5x - x = -3 - 3
4x = -6
x = -6 / 4
x = -3/2

Therefore, the solutions to the absolute value equation |5x + 3| = |3 - x| are x = 0 and x = -3/2.