Solve − 1 < − (1/x) + 2x < 1.
The method I chose initally was to mutliply the whole inequality by x only to realise x could be negative and so multiplied out by x^2.
-x2<-x+ 2x3< x2
0 < 2x3 + x2 - x < 2x2
I realised I couldn't do anything useful with the 2x2 as substracting it would give an inequality, where solutions for x could not be found ( please correct me if wrong)
I then thought to sketch f(x) = 2x3 + x2 - x , finding roots and y intercept,
and 2x2, aswell, finding where both functions instersect
and find the area where y values of f(x) are greater than zero but less than the 2x2 graph, and thus find the solutions for the corresponding x values.
My Question : Is there a quicker/easier method for finding solutions of x?
The method I chose initally was to mutliply the whole inequality by x only to realise x could be negative and so multiplied out by x^2.
-x2<-x+ 2x3< x2
0 < 2x3 + x2 - x < 2x2
I realised I couldn't do anything useful with the 2x2 as substracting it would give an inequality, where solutions for x could not be found ( please correct me if wrong)
I then thought to sketch f(x) = 2x3 + x2 - x , finding roots and y intercept,
and 2x2, aswell, finding where both functions instersect
and find the area where y values of f(x) are greater than zero but less than the 2x2 graph, and thus find the solutions for the corresponding x values.
My Question : Is there a quicker/easier method for finding solutions of x?