SOLUTION: Please solve this inequasion for me!!! |x+2|/|x-3|≤2
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Question 171637: Please solve this inequasion for me!!! |x+2|/|x-3|≤2
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
|x+2|/|x-3|≤2
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1st: x cannot be 3
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2nd: Solve the EQUALITY:
(x+2)/x-3) = 2
x+2 = 2x-6
x = 8
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If -2 < x < 3,
(x+2)/[-(x-3)] = 2
x+2 = -2x+6
3x = 4
x = 1.3333333...
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Plot those three values on a number line: 1.3333, 3, 8
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Check test values in the 4 resulting intervals to see where the solutions are.
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Check x = -10: |-10+2|/|-10-3| < = 2; true, so solutions in (-inf,1.3333]
Check x = 2 ; |2+2|/|2-3| = 4 < 2; false
Check x =5 ; |5+2|/|5-3| =7/2 < 2; false
Check x = 10 ; |10+2|/|10-3|=12/7 < 2; true, so solution in [8,+inf)
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Ans: (-inf,1.333]U[8,+inf)
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Cheers,
Stan H.
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