SOLUTION: Could some one help me understand this problem? The instructions are to solve the inequality. State the solution set using interval notation and graph it: x - 2/x + 3 is less t

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Could some one help me understand this problem? The instructions are to solve the inequality. State the solution set using interval notation and graph it: x - 2/x + 3 is less t      Log On


   

Question 18722: Could some one help me understand this problem?
The instructions are to solve the inequality. State the solution set using interval notation and graph it:
x - 2/x + 3 is less than 1
Thanks for the help
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
x - 2/x + 3 is less than 1
let y=(x - 2/x + 3)<1
x - 2/x + 3-1<0 ....or....x - 2/x + 2<0
(x^2-2+2x)/x<0...or ...(x^2+2x-2)/x<0..
now a fraction will be -ve (<0)if n.r and d.r are of different signs..let us take the 2 cases
dr=x is +ve...then nr should be -ve
dr=x is -ve...then nr should be +ve.
now solve the nr using quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A%28-2%29%29%29%2F%282%2A1%29+
hence x=(-1+sqrt3)/2...and....(-1-sqrt3)/2..for conveinience if we call these 2 values as p(approximately=-1.37)and q(approximately=0.37),we find that if x lies between p and q (-1.37 and 0.37 )nr is -ve and when x is less than
p(-1.37) or greater than q(0.37) ,nr is +ve.
now we have to combine this with the above assumption on dr
dr=x is +ve...then nr should be -ve..so x should be between 0 and (-1+sqrt3)/2(not -1.37 to zero as x is already taken as positive)
dr=x is -ve...then nr should be +ve.so x should be less than ....(-1-sqrt3)/2..
(not 0.37 to zero as x is already taken as negative)