SOLUTION: can anyone help me with that........ |x-1|/|x-5| < 3

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Question 878552: can anyone help me with that........

|x-1|/|x-5| < 3
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Both absolute values are positive quantities. Skipping the logic for the absolute values, These four inequality statements can be made:

x-1%3C3%28x-5%29 which gives x%3E7;
x-1%3C3%285-x%29 which gives x%3C4;
1-x%3C3%285-x%29 which gives x%3C7;
1-x%3C3%28x-5%29 which gives x%3E4;
and obviously from the original inequality, x%3C%3E5.

You find at x=4 or at x=7 that the inequality is false. This is in agreement with the separate solutions found as indicated.

Checking the interval between 4 and 7, the inequality is found false.
The inequality is found true for any x%3C4 or any x%3E7.

Finished solution is highlight%28x%3C4%29 OR highlight%28x%3E7%29.