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Unformatted text preview: fact. This is the important fact as it is often the most misused and/or forgotten fact in
solving inequalities.
If you aren’t sure that you believe that the sign of c matters for the second and third fact consider
the following number example. 3 < 5 I hope that we would all agree that this is a true inequality. Now multiply both sides by 2 and by
2. 3 < 5 3 < 5 3 ( 2 ) < 5 ( 2 ) 3 ( 2 ) > 5 ( 2 )  6 < 10 6 > 10 Sure enough, when multiplying by a positive number the direction of the inequality remains the
same, however when multiplying by a negative number the direction of the inequality does
change.
Okay, let’s solve some inequalities. We will start off with inequalities that only have a single
inequality in them. In other words, we’ll hold off on solving double inequalities for the next set
of examples.
The thing that we’ve got to remember here is that we’re asking to determine all the values of the
variable that we can substitute into the inequality and get a t...
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 Spring '12
 MrVinh

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