SOLUTION: Hi! I need help on an inequality involving absolute value. The problem is |(1/x)-3|>6. I broke the inequality into 2 equations, (1/x)-3>6 and (1/x)-3<-6. I then proceeded to ge

Question 564091: Hi!
I need help on an inequality involving absolute value. The problem is |(1/x)-3|>6. I broke the inequality into 2 equations, (1/x)-3>6 and (1/x)-3<-6. I then proceeded to get the equations, (1/x)>9 and (1/x)<-3. I am stuck from here. The answer I should get is (-(1/3),0) union (0,(1/9)). Thank you for any help you can give me.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
|(1/x)-3| > 6
---
The problem has 2 parts:
(1/x)-3 > 6 ; (1/x)-3 < -6
------------------------------
(1/x) > 9 ; (1/x) < -3
Notice x must equal 1/10, 1/11, 1/12 etc.(getting closer and closer to zero)
Notice x must equal -1/4, -1/5 , -1/6 etc.(getting closer and closer to zero)
----
-1/3< x < 0 ; 0< x < 1/9
----
Solution: (-1/3 , 0) U (0 , 1/9)
=============================================
Cheers,
Stan H.
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