Here, we see two numbers are being multiplied together in the inequality (
and 
). And we know that the only way to multiply two numbers together and get a number less than 0 is to multiply a positive and a negative number together. (positive * positive = positive; and negative * negative = positive)
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document.write( "Thus, we know that 
is true in either of the following situations:
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document.write( "1. 
and 
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document.write( "2. 
and
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document.write( "If you look at the first statement carefully, you may note that it can never be true. As previously stated, positive * positive = positive; and negative * negative = positive, so there is no way you can take any integer, square it, and get a negative number. This means, we only need to concern ourselves with the second situation, and .\r
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document.write( "So, let's solve the two inequalities:
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(get the square root of both sides)
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document.write( "So, we get as our answer. (because all items > -8 are also > 0, so we use the more restrictive option as our final answer to ensure all possibilities work.)
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document.write( "We can always double check our work. Let's take 
, as that satisfies our answer condition. Plugging it into our original inequality:
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, which is a true statement.
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document.write( "![\"\"](\"/images/stars/stars-05.gif\")
