Question

There is only one rule of balancing for which an equation and an inequality differ from each other. Discuss that rule.

Hint:the process involves a negative number

Answer 1

Look at this:

10 = 10 is a true equation.
Multiply both sides by -2:
-20 = -20 is also a true equation.
Now divide the original equation by -2
-5 = -5. Again this is a true equation.

Answer 2

When you divide by a negative and you are dealing with an inequality, you have to change the direction of the inequality :D.

So if you have y>-2x and you want to make x the subject, you divide throughout by -2 and you would end up with -2y<x because of that rule.

Answer 3

Now let's see what happens when you do this to an inequality.

5 < 10 is a true inequality
Multiply both sides by -2:
-10 < -20 is a false inequality.
Now divide the original inequality by -5:
-1 < -2 is also false.
Clearly, multiplying and dividing an inequality by a negative number has an effect different than when you do it to an equation.

Answer 4

If you have
5 < 10, a true inequality, and you multiply or divide both sides by a negative number, then you need to change the direction of the inequality sign.
5 < 10 is true
Multiply both sides by -2, and change < to >:
-10 > -20 is true.