SOLUTION: -3/5 < 1/5 - 2/15w < -1/3 Thank you for your help, this will help me for my study quiz tonight.

Algebra ->  Inequalities -> SOLUTION: -3/5 < 1/5 - 2/15w < -1/3 Thank you for your help, this will help me for my study quiz tonight.      Log On


   

Question 159863: -3/5 < 1/5 - 2/15w < -1/3
Thank you for your help, this will help me for my study quiz tonight.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

-3%2F5%3C1%2F5-%282%2F15%29w%3C-1%2F3 Start with the given inequality.


Multiply EVERY term by the LCD 15 to clear the fractions.


-9%3C3-2w%3C-5 Multiply and simplify


-12%3C-2w%3C-8 Subtract 3 from both sides.


6%3Ew%3E4 Divide both sides by -2. Note: this will flip the inequality signs



So the solution is 4%3Cw%3C6


So the answer in interval notation is ()


Also, the answer in set-builder notation is


Here's the graph of the solution set

Graph of the solution set

Note:
There is an open circle at w=4 which means that we're excluding this value from the solution set
Also, there is an open circle at w=6 which means that we're excluding this value from the solution set.