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