SOLUTION: Why does the inequality sign change when both sides are multiplied or divided by a negative number? Does this happen with equations? Why or why not? Write an inequality and use bot
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Question 176215: Why does the inequality sign change when both sides are multiplied or divided by a negative number? Does this happen with equations? Why or why not? Write an inequality and use both multiplication and addition properties of inequalities. Answer by solver91311(24713) (Show Source):
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Think about the statement . This statement is clearly true. But if you multiply both sides by , you get which is no longer a true statement until you also reverse the sense of the inequality, namely .
Another way to think about it is to consider the statement . This statement is true if and only if is to the left of on the number line. But if you multiply by , you now have to the right of on the number line and therefore .
As for equations, the only way you can change an equal sign is to make it a NOT equal sign. Multiplying both sides of an equation by a negative number doesn't make the two sides unequal, so the equal sign does not change.
You can make up your own inequality as an example.
