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You must reverse the sense of inequality because, in essence, you're taking the opposite of both sides. In order to more properly show this, here's an example. 3>2 Three is greater than two. True statement, right? Let's multiply both sides by -1 -3>-2 The statement is no longer true. In order to keep the equation true, you must flip the inequality. As in -3<-2 Now, the statement is true again.
To make inequalities that are not true into true statements, you would need to manipulate the inequality by performing the same operation on both sides. For example, if you have the inequality 4 > 6, you could subtract 2 from both sides to get 2 > 4, which is still not true. You could then multiply both sides by -1 to get -2 < -4, which is a true statement. By understanding the properties of inequalities and performing operations that maintain the inequality's direction, you can transform false inequalities into true ones.
That is called an inequality.
-4 < 9
a statement that two quantities are unequal, indicated by the symbol I found this at http://dictionary.reference.com/browse/inequality