<PRE><B>Question 67163</B>
&lt;pre&gt;&lt;font size = 5&gt;&lt;b&gt;
How would I solve the inequality 7&lt;4x+3&lt;u&gt;&lt;&lt;/u&gt;21 and 
express the solution as an interval?

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 7 &lt; 4x + 3 &lt;u&gt;&lt;&lt;/u&gt; 21

The idea is to isolate x in the middle.
Get rid of the 3 by adding -3 to all three sides:

  7 &lt; 4x + 3 &lt;u&gt;&lt;&lt;/u&gt; 21
 -3       -3   -3
-------------------
  4 &lt; 4x     &lt;u&gt;&lt;&lt;/u&gt; 18

So we have
 
    4 &lt; 4x &lt;u&gt;&lt;&lt;/u&gt; 18

Now we divide all three sides by the coefficient of x,
which is 4.  Since we are dividing by a positive
number we DO NOT reverse the inequalities as we do
when we divide thru by a negative number:

    4     4x     18
   ЧЧЧ &lt; ЧЧЧЧ &lt;u&gt;&lt;&lt;/u&gt; ЧЧЧЧ
    4      4      4

or
                 9  
        1 &lt; x &lt;u&gt;&lt;&lt;/u&gt; ЧЧЧ
                 2
or

        1 &lt; x &lt;u&gt;&lt;&lt;/u&gt; 4.5



On a number line this is graphed as

--------------o=============&lt;font face = &quot;symbol&quot;&gt;╖&lt;/font&gt;------------
 -2  -1   0   1   2   3   4   5   6   7          

It is an open circle at 1, because
it is &lt; and not &lt;u&gt;&lt;&lt;/u&gt;, and closed (dark
circle) at 4.5, because it is &lt;u&gt;&lt;&lt;/u&gt; and not &lt;.

The interval notation is a shorthand
for this graph:

       (1, 4.5]

The &quot;(&quot; on the left represents the
open circle, the 1 is the left endpoint
of the shaded part, the 4.5 is the right endpoint
of the shaded part, and the &quot;]&quot; represents
the closed circle.

Edwin&lt;/pre&gt;
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