Find all solutions to equation

[dusky seal]

h(x) =|x|-3x+4
h(x-1) = x-2

Solving this yields 8/3 and 2.
Why 2 is not a solution? How to validate solutions?

[fallen grotto]

1. Wait patiently for a helper to come along.
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[dusky juniper]

Hm, let's see.
As far as I understand, you mean the following:
|x - 1| - 3(x - 1) + 4 = x - 2
Simplifying it a bit gives:
|x - 1| - 4x + 9 = 0
Case 1. x ≥ 1.
x - 1 - 4x + 9 = 0
3x = 8
x = 8/3
This satisfies x ≥ 1, so we keep this root.
Case 2. x ≤ 1.
1 - x - 4x - 9 = 0
5x = 10
x = 2
This doesn't satisfy x ≤ 1, so we discard this root.
Thus, the only root is x = 8/3.

[dusky seal]

Thank you.