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

Algebra ->  Inequalities -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!

Think about the statement 3+%3E+2. This statement is clearly true. But if you multiply both sides by -1, you get -3+%3E+-2 which is no longer a true statement until you also reverse the sense of the inequality, namely -3+%3C+-2.

Another way to think about it is to consider the statement a+%3E+b. This statement is true if and only if a is to the left of b on the number line. But if you multiply by -1, you now have -a to the right of -b on the number line and therefore -a+%3C+-b.

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.