SOLUTION: 1/8 x is greater than or equal to - 3/16

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Question 621563: 1/8 x is greater than or equal to - 3/16
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
(I've corrected my error.~AF)
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Hi, there--
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I'm not sure if your problem is this,
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1%2F%288x%29%3E=-%283%29%2F%2816%29
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or this,
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%281%2F8%29x%3E=-%283%29%2F%2816%29
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I've solved them both below. Take your pick...
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FIRST PROBLEM:
1%2F%288x%29%3E=-%283%29%2F%2816%29
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We want to simplify this equation by clearing the denominators. Multiply both sides of the equation by 16.
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%28%281%29%2816%29%29%2F%288x%29%3E=-%28%283%29%2816%29%29%2F%2816%29
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Simplify. On the right side of the equation, you have 16 in the numerator divided by 16 in the denominator. Since 16/16=1, they cancel each other out.
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%2816%29%2F%288x%29%3E=-3
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Repeat the process by multiplying both sides of the equation by 8x.
%28%2816%29%288x%29%29%2F%288x%29%3E=-3
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As before, we can cancel the 8x in the numerator and the denominator because 8x/8x=1.
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16%3E=%28-3%29%288x%29
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Simplify.
16%3E=-24x
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Divide both sides of the equation by -24. IMPORTANT NOTE: When you multiply or divide an inequality by a negative number, the direction of the inequality changes. ("greater than or equal to" becomes "less than or equal to.")
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x%3C=%2816%29%2F%28-24%29
x%3C=-%282%2F3%29
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SECOND PROBLEM:
%281%2F8%29x%3E=-%283%29%2F%2816%29
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We want to isolate the variable x on the left side of the equation. We multiply both sides by 8 because 8 is the reciprocal of 1/8. (8 times (1/8) is 1.)
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x%3E=-%28%283%29%288%29%29%2F%2816%29
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Simplify.
x%3E=-%2824%29%2F%2816%29
x%3E=-%283%29%2F%282%29
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Hope this helps! Feel free to email if there is any part you don't understand yet.
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~Ms.Figgy
math.in.the.vortex@gmail.com