Question

`|3 - x| - (x - 1) = 4`
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Answer 1

`x=0`

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.

`|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\\eq 3\\\\x=0\\-3\\eq 3\\`

Therefore, the solution is
`x=0`