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-3n < 81
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\n" ); document.write( "You need to solve this inequality for +n. You can operate on the inequality just as you would
\n" ); document.write( "an equation ... with a single exception ... that exception is that if you multiply or divide
\n" ); document.write( "both sides of the inequality by a negative number you have to also reverse the direction of
\n" ); document.write( "the inequality sign.
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\n" ); document.write( "This being the case, you can solve the given inequality by dividing both sides by -3, the
\n" ); document.write( "multiplier of the n term. When you divide both sides by -3 (and reversing the direction
\n" ); document.write( "of the inequality sign because you are dividing by a negative number), the resulting
\n" ); document.write( "inequality is:
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\n" ); document.write( "and the right side simplifies to:
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\n" ); document.write( "That means that the original inequality will be true as long as n is greater than -27.
\n" ); document.write( "That means that if n is a value to the right of -27 on the number line, the inequality
\n" ); document.write( "will be true. Let's try a couple of values just to help convince ourselves that our answer
\n" ); document.write( "is correct. For example, what happens if n is -28 ... put -28 in for n in the original
\n" ); document.write( "inequality ... and it becomes:
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\n" ); document.write( "(-3)*(-28) < 81
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\n" ); document.write( "Multiply out the left side and you get:
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\n" ); document.write( "+ 84 < 81
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\n" ); document.write( "This obviously is not true ... and that should be no surprise because we had found that
\n" ); document.write( "n had to be greater than -27 to work. So let's try n = -26 ... that's a value of n
\n" ); document.write( "that is greater than -27 and so it should work. Substitute - 26 for n in the original
\n" ); document.write( "inequality and you get:
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\n" ); document.write( "(-3)*(-26) < 81
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\n" ); document.write( "Multiply out the left side and you get:
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\n" ); document.write( "+78 < 81
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\n" ); document.write( "That is true ... 78 is less than 81. Therefore, we have a couple of examples that help
\n" ); document.write( "to confirm that if n is greater than -27 it works, but if n is less than -27 it does not
\n" ); document.write( "work.
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\n" ); document.write( "It never hurts to check a few values to confirm your answer.
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\n" ); document.write( "Hope this shows you that you can work inequalities as you would an equation ... except
\n" ); document.write( "for dividing and multiplying by negative numbers. \n" ); document.write( "