Answer:
[tex]x=0[/tex]
Step-by-step explanation:
Evaluate all the arithmetic first, and then remember absolute value equations have two possible ways to go (+ and -).
You can see how I split them on the 3rd line, later demonstrating how the 2nd one is invalid.
[tex]|3-x|-x+1=4\\\\|3-x|-x=3\\\\3-x-x=3\\-(3-x)-x=3\\\\3-2x=3\\-3+x-x=3\\\\-2x=0\\-3\neq 3\\\\x=0\\-3\neq 3\\[/tex]
Therefore, the solution is [tex]x=0[/tex]
