SOLUTION: Solve 2/x (lesser to equal than sign) x/2 Plot on number line too!

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Question 1115838: Solve 2/x (lesser to equal than sign) x/2
Plot on number line too!
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(53751) About Me  (Show Source):
You can put this solution on YOUR website!
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Sorry,
I am cleaning the posts after some malicious user.


Answer by josgarithmetic(39794) About Me  (Show Source):
You can put this solution on YOUR website!
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2%2Fx is less than or equal to x%2F2.
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2%2Fx%3C=x%2F2
-
2%2Fx-x%2F2%3C=0
%282%2Fx%29%282%2F2%29-%28x%2F2%29%28x%2Fx%29%3C=0
4%2F%282x%29-x%5E2%2F%282x%29%3C=0
%284-x%5E2%29%2F%282x%29%3C=0

highlight_green%28%28%282-x%29%282%2Bx%29%29%2F%282x%29%3C=0%29

The critical values of x can be found from that inequality.
These critical x values are -2, 0, 2.

check the intervals on x in -infinity%3Cx%3C=-2, -2%3C=x%3C0,0%3Cx%3C=2, 2%3C=x%3Cinfinity.
See in which intervals the ORIGINAL inequality is true and in which it is false.


TRUE FOR -2%3C=x%3C0 and for 2%3C=x%3Cinfinity.