Question 245249: Solve the inequality:
|x+12/x-12|< or equal to 3
Please help
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Solve the inequality:
|x+12/x-12|<= 3
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Looking you can see that x cannot be 12.
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Solving the EQUALITY you gt:
(x+12)/(x-12) = 3 or (x+12)/(x-12) = -3
x+12 = 3x-26 or x+12 = -3x+36
2x = 38 or 4x = 24
x = 19 or x = 6
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So, draw a number line and plot x = 6, x = 12, x = 19
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Now find the solutions for the INEQUALITY by checking
a value in each of the four resulting intervals of
the number line.
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|x+12/x-12| < 3
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Let x = 0; you get |12/-12| < 3 ; true, so solutions in (-inf,6)
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Let x = 10; you get |22/-2} < 3 ; false, so no solutions in (6,12)
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Let x = 15; you get |27/3| < 3 ; false, so no solutions in (12,19)
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Let x = 25 ; you get |37/13| < 3 ; true, so solutions in (19,+inf)
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Combining the solutions for the EQUALITY and the INEQALITY you get:
(-inf,6] U [19,+inf)
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Cheers,
Stan H.
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