```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>

```