SOLUTION: Solve the inequality state the solution set in interval notation and sketch its graph - 3/5<1/5 – 2/15w<- 1/3 Thanks!!

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Question 83525: Solve the inequality state the solution set in interval notation and sketch its graph
- 3/5<1/5 – 2/15w<- 1/3
Thanks!!
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

Solve the inequality state the solution 
set in interval notation and sketch its graph

                -3%2F5 < 1%2F5 - 2%2F15w < -1%2F3


Clear of fractions by multiplying all terms on 
all three sides by the LCD of 15

         15%28-3%2F5%29 < 15%281%2F5%29 - 15%282%2F15%29w < 15%28-1%2F3%29

                  -9 < 3 - 2w < -5

Solve for w in the middle:  Add -3 to all three sides:

                  -9 < 3 - 2w < -5
                  -3  -3        -3
                --------------------
                 -12 <    -2w < -8

Divide all three sides by the coefficient of w, which is -2.
Remember that dividing through an inequality by a negative
causes the inequality symbols to switch directions:

                 %28-12%29%2F%28-2%29 > %28-2w%29%2F%28-2%29 > %28-8%29%2F%28-2%29

or simplifying:

                            6 > w > 4   <-----solution
  
which is the same as

                            4 < w < 6   <-----solution

whose number line graph is

       -------------------o=====o---------------   <-----graph
       -2 -1  0  1  2  3  4  5  6  7  8  9 10 11 

The interval notation is an abbreviation for that graph:

                              (4, 6)   <-----solution in interval       
                                                       notation
Edwin