When Do You Flip an Inequality Sign?
Date: 12/19/2005 at 21:28:17 From: Oscar Subject: what does it mean to change the sense of inequality? What does it mean to change the sense of an inequality? I just started studying about inequalities, and I can't grasp the concept of that question I found in the book. I would really like to know if anyone can help out please.
Date: 12/19/2005 at 22:57:13 From: Doctor Peterson Subject: Re: what does it mean to change the sense of inequality? Hi, Oscar. Your book probably defined what they mean by "the sense of an inequality", but it may be hard to find or hard to follow without some examples. The "sense" of an inequality, also called its "direction", means whether it is < or >. We change its sense when we change > into < or vice versa. We can do that for two reasons, which are alternative ways to solve certain inequalities. One is when we just want to rewrite an inequality so that it reads more naturally: 3 < x becomes x > 3 These mean the same thing, but the first sounds like it is telling you where 3 is (3 is less than x), while the second sounds like a proper answer to the question "where is x?" (x is greater than 3). We've flipped the whole inequality around, including changing the direction of the "<". The other reason for changing the sense is when we multiply both sides of an inequality by a negative number. Notice that -2 < 3 but when we multiply both sides by -2, the order changes: 4 > -6 We have sort of flipped the whole number line around backward when we did the multiplication, so that the number that was on the left is now on the right. That means we have to change the sense when we multiply (or divide, which is a form of multiplication) by a negative number. Does that help? If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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