Why does the inequality sign change when both sides are multiplied or divided by a negative number? Does this happen with equations? Explain

Answer 1

Multiplying by a negative number is just a quick way of moving things to the other side of the inequality. Consider

-2x < 100

Now, you could solve it without doing any negative multiplying at all: just add 2x to both sides to get

0 < 2x + 100

Now subtract the 100 to get

-100 < 2x
or,
2x > -100

changing the sense of the inequality just means that terms have switched sides in the expression as written.

Answer 2

thank you!