SOLUTION: 2/x+1 < 4/4x-2 Factional Inequality
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Question 1120317: 2/x+1 < 4/4x-2 Factional Inequality
Found 2 solutions by solver91311, ikleyn:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Find all critical points:
Zeros:
Undefined Points:
is undefined at 
is undefined at 
Divide the 
-axis into 4 intervals:
Select four values, one from each interval that is not an endpoint of the interval and define \ =\ \frac{2}{x\ +\ 1}\ \ )
and \ =\ \frac{4}{4x\ -\ 2})
.
The original inequality is true wherever \ -\ g(x)\ >\ 0)
\ -\ g(-2)\ =\ -1\ -\ \frac{2}{5}\ <\ 0)
\ -\ g(0)\ =\ 2\ +\ 2\ >\ 0)
\ -\ g(1)\ =\ 1\ -\ 2\ <\ 0)
\ -\ g(3)\ =\ \frac{1}{2}\ -\ \frac{2}{5}\ >\ 0)
The solution set is then:
John
My calculator said it, I believe it, that settles it
Answer by ikleyn(52867) (Show Source): You can put this solution on YOUR website!
.
Be aware: The answer by @solver91311 is INCORRECT.
The correct solution obtained by @greenestamps is under this link
https://www.algebra.com/algebra/homework/Inequalities/Inequalities.faq.question.1120318.html
https://www.algebra.com/algebra/homework/Inequalities/Inequalities.faq.question.1120318.html
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