Because in Case 2 you require the denominator to be negative.
Prove It's method is very nice.
You could also consider this method to avoid making a lot of calculations....
Start by examining the denominator and realise that if
the denominator is always negative.
The numerator will always be positive as , so we have
All negative numbers are less than 2, hence if
Now, examine the denominator being positive. This happens when
When the denominator is positive, we can multiply both sides by the denominator
Therefore, the other solution is
This method also avoids the mess of multiplying across by a negative denominator and reversing inequality signs.