The quotient of a number an -2 is less than 30

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

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

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.

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step-by-step explanation: