Your expression is written (where n represents the number) ...
... n/(-2) < 30
This is solved by multiplying both sides of the inequality by -2. Multiplying by a negative number reverses the inequality symbol, so you have
... n > -60 . . . . . the solution
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You can check this easily enough. For example, n = -58 > -60. Then you have
... -58/-2 < 30
... 29 < 30 . . . . . . . true
Or, for positive numbers n, n = 150 > -60.
... 150/-2 < 30
... -75 < 30 . . . . . . . true
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You might wonder why multiplication (or division) by a negative number reverses the sense of the inequaltiy. Consider multiplication by -1. That effectively reflects the relationship across the 0 point (origin) of the number line. For example, if you have
... 1 < 2
and you multiply by -1, then you have
... -1 > -2
If you plot the points on the number line, you see that
... 0 . . . 1 . . . 2
became
... -2 . . . -1 . . . 0
and the order of the numbers is reversed left-to-right. So, the greater than/less than relationship was also reversed.
