Gather Toward the Larger

In 5 - x < 2x - 4, the x-terms are -x on the left and 2x on the right. Collect them on the side with the larger coefficient. Here that is the right side, because 2 is larger than -1. Then the coefficient stays positive and you never need to flip the sign. Add x to both sides:

5 < 3x - 4

9 < 3x

3 < x

The last line says that 3 is less than x. Written with x first, it is x > 3.

You could collect the x-terms on the left instead. Subtracting 2x from both sides and then subtracting 5 gives -3x < -9. Dividing by -3 and flipping the sign gives x > 3 again. Both ways give the same answer. Collecting toward the larger coefficient avoids the division by a negative number.