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

Algebra ->  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

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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(21667) 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.


15%28-3%2Fcross%285%29%29%3C15%281%2Fcross%285%29%29-15%28%282%2Fcross%2815%29%29w%29%3C15%28-1%2F3%29 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

drawing%28500%2C80%2C-1%2C+11%2C-10%2C+10%2C%0D%0Anumber_line%28+500%2C+-1%2C+11+%29%2C%0D%0A%0D%0Ablue%28line%284%2C0%2C6%2C0%29%29%2C%0D%0Ablue%28line%284%2C0.30%2C6%2C0.30%29%29%2C%0D%0Ablue%28line%284%2C0.15%2C6%2C0.15%29%29%2C%0D%0Ablue%28line%284%2C-0.15%2C6%2C-0.15%29%29%2C%0D%0Ablue%28line%284%2C-0.30%2C6%2C-0.30%29%29%2C%0D%0Acircle%284%2C0%2C0.25%29%2Ccircle%284%2C0%2C0.20%29%2C%0D%0Acircle%286%2C0%2C0.25%29%2C%0D%0Acircle%286%2C0%2C0.20%29%0D%0A%0D%0A%29 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.