SOLUTION: Question: When we multiply or divide on both sides by a negative number we must reverse the inequality symbol. I understand why this needs to be done. But why do we not have to do

Question 178185: Question: When we multiply or divide on both sides by a negative number we must reverse the inequality symbol. I understand why this needs to be done. But why do we not have to do this when we are working with equations? Or do we do this with equations?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

If you reverse the inequality sign, you reverse the sense of the inequality. But you can't 'reverse' an equals sign. Equals is equals.

Think about the reason that we reverse the inequality:

is certainly a true statement, but multiplying by -1 gives us:

which is no longer true until you reverse the sign:

But consider a statement containing equals:

is true, and if you multiply by -1,

is still true.

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