<PRE><B>Question 33456</B>
&lt;pre&gt;&lt;b&gt;&lt;font size = 4&gt;Solve the inequality:

2/3(3x-9) &lt;u&gt;&lt;&lt;/u&gt; 8

Use the distributive law to get rid of the parentheses.

            2/3(3x-9) &lt;u&gt;&lt;&lt;/u&gt; 8

(2/3)(3x) + (2/3)(-9) &lt;u&gt;&lt;&lt;/u&gt; 8

            2x + (-6) &lt;u&gt;&lt;&lt;/u&gt; 8

               2x - 6 &lt;u&gt;&lt;&lt;/u&gt; 8

Add 6 to both sides

                   2x &lt;u&gt;&lt;&lt;/u&gt; 14

Divide both sides by 2

                    x &lt;u&gt;&lt;&lt;/u&gt; 7

That may be all your teacher wants. But sometimes 
they want you to do more.

If you are asked for the solution set than that is 

      {x|x is real and x &lt;u&gt;&lt;&lt;/u&gt; 7}

The way that is read is:

&quot;The set of all x such that x is a real number which
is less than or equal to seven&quot;.

If you are asked for more, i.e., then read the rest. 
Draw the graph on a number line, and/or give the 
solution in set-builder notation as well as in interval
notation.

The graph on a number line is done this way:

First we draw a number line:

ЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧ
-3 -2 -1  0  1  2  3  4  5  6  7  8  9  10 11

Then we draw a circle at 7, but we have to go by this rule
to determine whether we will use an open circle like this &quot;o&quot; 
or a closed circle like this &quot;&lt;font face =&quot;wingdings&quot;&gt;l&lt;/font&gt;&quot;.  The rule is if it&#39;s &quot; &lt; &quot; or
&quot; &gt; &quot; then we use an open circle &quot;o&quot; and if its &lt;u&gt;&gt;&lt;/u&gt; or &lt;u&gt;&lt;&lt;/u&gt;,
then we use &lt;font face =&quot;wingdings&quot;&gt;l&lt;/font&gt;. So since this is a case of &lt;u&gt;&lt;&lt;/u&gt;, we use &quot;&lt;font face =&quot;wingdings&quot;&gt;l&lt;/font&gt;&quot;   

ЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧ&lt;font face =&quot;wingdings&quot;&gt;l&lt;/font&gt;ЧЧЧЧЧЧЧЧЧЧЧЧЧ
-3 -2 -1  0  1  2  3  4  5  6  7  8  9  10 11

Now we use this rule:

If it&#39;s &gt; or &lt;u&gt;&gt;&lt;/u&gt; then you shade to the right because it&#39;s
&quot;greater than&quot; and the greater numbers are to the right.

If it&#39;s &lt; or &lt;u&gt;&lt;&lt;/u&gt; then you shade to the left because it&#39;s
&quot;less than&quot; and the lesser numbers are to the left.

So we shade to the right:
                                                             
ЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧ&lt;font face =&quot;wingdings&quot;&gt;lnnnnnnnnnnnnn&lt;/font&gt;&gt;
-3 -2 -1  0  1  2  3  4  5  6  7  8  9  10 11                  

That&#39;s the graph.  The interval notation is 

                      [7,&lt;font face = &quot;symbol&quot;&gt;е&lt;/font&gt;) 

If it had been x &gt; 7, then the graph would have been this:

ЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧЧ&lt;font size = 6&gt;o&lt;/font&gt;&lt;font face =&quot;wingdings&quot;&gt;nnnnnnnnnnnnn&lt;/font&gt;&gt;
-3 -2 -1  0  1  2  3  4  5  6  7  8  9  10 11  

and the interval notation would have been 

                      (7,&lt;font face = &quot;symbol&quot;&gt;е&lt;/font&gt;)
Edwin
AnlytcPhil@aol.com
&lt;/pre&gt;

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