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Given:
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\n" ); document.write( "You basically can work inequalities using the same procedures that you would for solving
\n" ); document.write( "an equation ... with this exception ... if you multiply or divide both sides of the
\n" ); document.write( "inequality by a negative quantity, you must reverse the direction of the inequality sign.
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\n" ); document.write( "We want to solve this inequality for +x, so we need to get +x on one side of the inequality
\n" ); document.write( "sign and everything else on the other side. To isolate +x, let's divide both sides of
\n" ); document.write( "inequality by
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\n" ); document.write( "But since we divided both sides by a negative, we must reverse the direction of the
\n" ); document.write( "inequality sign. So the actual form should be:
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\n" ); document.write( "Recall the arithmetic rule that when you divide by a fraction you can get the same result
\n" ); document.write( "by inverting the fraction and multiplying. Using this rule results in the right side of
\n" ); document.write( "the inequality becoming:
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\n" ); document.write( "Note that a minus times a minus equals a + quantity. So
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\n" ); document.write( "Substitute this into the inequality for the right side and you have:
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\n" ); document.write( "So it appears that x must be greater than 16 if it is to satisfy the original expression.
\n" ); document.write( "Let's try it and see. The original expression was:
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\n" ); document.write( "Since we said that x must be greater than 16, let's try letting x = 20. This makes the
\n" ); document.write( "inequality become:
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\n" ); document.write( "Multiplying the left side results in -15. So the inequality is:
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\n" ); document.write( "That is true because -15 is to the left of -12 on the number line ... so it is less than -12.
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\n" ); document.write( "Now let's try letting x be a number less than 16. Suppose we let x = 12. The original
\n" ); document.write( "inequality becomes:
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\n" ); document.write( "Multiplying out the left side results in:
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\n" ); document.write( "This is NOT true because -9 is not to the left of -12 on the number line. Therefore,
\n" ); document.write( "numbers less than 16 do not seem to work in the inequality. Our answer that x must be
\n" ); document.write( "greater than 16 seems to work for this problem. Hope this helps you to understand a
\n" ); document.write( "few of the basics of working with inequalities. \n" ); document.write( "