Question 83525
<pre><font face = "lucida console" size = 4>
Solve the inequality state the solution 
set in interval notation and sketch its graph

                {{{-3/5}}} < {{{1/5}}} - {{{2/15}}}w < {{{-1/3}}}


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

         15{{{(-3/5)}}} < 15{{{(1/5)}}} - 15{{{(2/15)}}}w < 15{{{(-1/3)}}}

                  -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:

                 {{{(-12)/(-2)}}} > {{{(-2w)/(-2)}}} > {{{(-8)/(-2)}}}

or simplifying:

                            6 > w > 4   <font color = "red"><-----solution</font>
  
which is the same as

                            4 < w < 6   <font color = "red"><-----solution</font>

whose number line graph is

       -------------------o=====o---------------   <font color = "red"><-----graph</font>
       -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)   <font color = "red"><-----solution in interval       
                                                       notation</font>
Edwin</pre>