SOLUTION: Solve the inequality |x/x-1|<2 by interpreting the absolute value function as a distance function.

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Question 926070: Solve the inequality |x/x-1|<2 by interpreting the absolute value function as a distance function.
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
What is a "distance function"?
Whatever, the written equation seems wrong, otherwise it would simply mean |0|<2, which would be a correct statement but not likely what you were really given.


abs%28x%2F%28x-1%29%29%3C2,
two critical values are 0 and 1. Check the three intervals which these two values create.

x%3C0%2C
abs%28-2%2F%28-2-1%29%29=abs%282%2F3%29=2%2F3%3C2, TRUE.

0%3Cx%3C1
abs%280.5%2F%280.5-1%29%29=abs%280.5%2F%28-0.5%29%29=1%3C2, TRUE.

1%3Cx
abs%283%2F%283-1%29%29=abs%283%2F2%29=3%2F2%3C2, TRUE.

The given inequality seems to be true for all x values BUT highlight%28x%3C%3E1%29.