Why it is necessary to reverse the inequality symbol when multiplying?

Question

Why it is necessary to reverse the inequality symbol when multiplying both sides of an inequality by a negative number?

Can you give an example!!!

Answer 1

View the inequality as two knots in a string extending away from you through a zero point. One represents a larger value and the other a smaller value.

Changing the signs is equivalent to swinging the string 180 degrees around the zero point. The one that was closer to you is now the one farther away and vice versa. This means that the value that was larger is now smaller, etc.

The other responder's examples are good ones.

Answer 2

It's because multiplying (or dividing) by a negative switches that number to the other side of the number line. When both numbers switch relative to zero, they end up on opposites sides of each other. It's probably easiest to see with regular numbers (i.e. no variables). Take the statement: 3 > 2 Now if you multiply both sides by -1, you get: -3 > -2 That would be incorrect unless you switched the sign: -3 < -2 That makes more sense... Here's another example: 4 > -1 Multiply by -1 and you'll need to switch the inequality symbol: -4 < 1 Got it?

Answer 3

To uphold truth
It is a fact that 2 > 1
It is however not true that -2 > -1
The truth is -2 < -1

I've also seen someone else do this:
2 > 1
subtract 3 from both sides
-1 > -2
or -2 < -1

Answer 4

1 < 2
-1 > -2

-1 < 2
1 > -2

Answer 5

3<4, represent the two numbers on a real line. 4 is on the right of 3
multiply both sides by -1;
-3>-4. -3 is on the right of -4.ANS.