How to solve for x as a denominator in an inequality?

Examples:

2/x < 4 ... multiply both sides by x, cancelling it on the left side

2 < 4x ... now divide by 4

2/4 < x

1/2 < x

5/x + 7 > = 12

5/x > = 12 - 7

5/x > = 5 ... multiply by x, cancelling it on the left

5 > = 5x ... divide by 5

5/5 > = x

1 > = x