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How do signs change in an inequality?

Normal manipulation of inequalities does not affect the direction of the inequality such as:
addition
subtraction
multiplication or division by a positive number, 

 

The direction of the inequality will change by:
multiplication or division of a negative number
swapping the sides of the inequality

 

This can also be thought of a sign change, where the sides are swapped back to their original sides, but the signs change.

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