SOLUTION: 11. Solve the following inequality and write your answer using interval notation. Please show all of your work. (x/5)< 3/(6x-1) THANK YOU!!!!!

Algebra ->  Inequalities -> SOLUTION: 11. Solve the following inequality and write your answer using interval notation. Please show all of your work. (x/5)< 3/(6x-1) THANK YOU!!!!!      Log On


   

Question 558142: 11. Solve the following inequality and write your answer using interval notation. Please show all of your work.
(x/5)< 3/(6x-1)
THANK YOU!!!!!
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
x%2F5 < 3%2F%286x-1%29

x%2F5 - 3%2F%286x-1%29 < 0

The LCD = 5(6x-1)

x%2F5·%286x-1%29%2F%286x-1%29 - 3%2F%286x-1%29·5%2F5 < 0

%286x%5E2-x%29%2F%285%286x-1%29%29 - 15%2F%285%286x-1%29%29 < 0

%286x%5E2-x-15%29%2F%285%286x-1%29%29 < 0

%28%283x-5%29%282x%2B3%29%29%2F%285%286x-1%29%29 < 0

"< 0" means negative, so we want the left side to be negative.

Find the critical values by setting numerator = 0 and
denominator = 0
                 
There are 3 critical numbers, 5%2F3, -3%2F2, and 1%2F6

In mixed fractions, they are 1%262%2F3, -1%261%2F2, and 1%2F6

We make this chart

 

The left side is negative on the intervals x%3C-1%261%2F2, and 1%2F6%3Cx%3C1%262%2F3

%28matrix%281%2C3%2C-infinity%2C+%22%2C%22%2C+-1%261%2F2%29%29 U %28matrix%281%2C3%2C1%2F6%2C%22%2C%22%2C1%262%2F3%29%29

Edwin