posted by Nini on .
Why does the inequality sign change when both sides are multiplied or divided by a negative number? Does this happen with equations? Explain
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
2x > -100
changing the sense of the inequality just means that terms have switched sides in the expression as written.