SOLUTION: abs(x+1)/abs(x-1)>=2

Algebra ->  Absolute-value -> SOLUTION: abs(x+1)/abs(x-1)>=2      Log On


   

Question 972466: abs(x+1)/abs(x-1)>=2
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
abs%28x%2B1%29%2Fabs%28x-1%29%3E=2

Absolute values are always positive.

abs%28x%2B1%29%3E=2%2Aabs%28x-1%29
2%2Aabs%28x-1%29-abs%28x%2B1%29%3C=0

Critical x values are -1 and 1.

x less than or equal -1,
pick -2 as example,
2%2Aabs%28-2-1%29-abs%28-2%2B1%29%3C=0 ?
2%2A3-1%3C=0
6-1%3C=0, FALSE

x between -1 and 1,
pick 0,
2%2Aabs%280-1%29-abs%280%2B1%29
2-1%3C=0, FALSE

x greater than or equal 1,
pick 2
2abs%282-1%29-abs%282%2B1%29%3C0
2-3%3C=0
-1%3C=0, TRUE.

SOLUTION should be , highlight%28x%3E=1%29.