You have done the process correctly. Now you need to understand what this implies.

You got x <= 7

Case 1: x-1< 0
When x-1< 0; x < 1
Note that when x-1 is negative, it will always be less than \(\sqrt{(7-x)}\)
So whenever x<1, the inequality will always hold.

Case 2: x-1 >= 0
If x-1 is non negative, we can square the inequality.
From this, you get -2<x<3.
The inequality holds in this range.

From the two cases, we see that the inequality holds for the range x < 3.
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