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April 1, 2015

Posted by **wade** on Tuesday, January 3, 2012 at 1:06pm.

- algebra -
**Reiny**, Tuesday, January 3, 2012 at 1:26pmtake any true inequality, say ...

4 < 10

now multiply both sides by 10

40 < 100 , still true

divide original by 2

2 < 5 , still true

multiply original by -10

-40 < -100 , FALSE!, how do we make it true ?

-40 > -100

divide original by -2

-2 < -5 , FALSE! , how do we make it true?

-2 > -5

what about equations?

5 = 5 , true

multiply by -1

-5 = -5, (did you notice how I switched the = sign from = to = ?? , lol)

- algebra -
**Steve**, Tuesday, January 3, 2012 at 2:19pmAnother way to think of this changing direction stuff is to leave the direction the same, and move the expressions. Suppose you have

-3x > 9

Rather than dividing by -3, let's get rid of the negative coefficient by adding and subtracting.

Add 3x to both sides:

-3x + 3x > 9 + 3x

0 > 9 + 3x

Now subtarct 9 from both sides

0 - 9 > 9 + 3x - 9

-9 > 3x

Now divide by +3 to get

-3 > x

So, what we have is

-3x > 9 changes to

-3 > x

and even though we haven't change direction of the actual symbol, we have done it logically by moving things to the other side of the arrow.

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