Question 49656
<pre><font size = 5><b>solve for x  

9(5x - 3) + 5(2x + 4) = 2(3x + 3)

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Multiply the 9 by the 5x, getting 45x.  So far we have:

<font color = "blue">45x</font>

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9(5x - 3) + 5(2x + 4) = 2(3x + 3)

Multiply the 9 also by the -3.  So far we have:

<font color = "blue">45x - 27</font>

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9(5x - 3) + 5(2x + 4) = 2(3x + 3)

Multiply the +5 by the 2x.  So far we have:

<font color = "blue">45x - 27 + 10x</font>

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9(5x - 3) + 5(2x + 4) = 2(3x + 3)

Multiply the +5 also by the +4.  So far we have:

<font color = "blue">45x - 27 + 10x + 20</font>

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9(5x - 3) + 5(2x + 4) = 2(3x + 3)

Copy the equal sign:

So far we have:

<font color = "blue">45x - 27 + 10x + 20 =</font>

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9(5x - 3) + 5(2x + 4) = 2(3x + 3)

Multiply the 2 by the 3x.  So far we have:

<font color = "blue">45x - 27 + 10x + 20 = 6x</font>

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9(5x - 3) + 5(2x + 4) = 2(3x + 3)

Multiply the 2 also by the +3.  So far we have:

<font color = "blue">45x - 27 + 10x + 20 = 6x + 6</font>

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<font color = "blue">45x - 27 + 10x + 20 = 6x + 6</font>

Now combine the 45x and the +10x. So far we have

<font color = "blue">      55x - 27 + 20 = 6x + 6</font>

Now combine the -27 and the +20:

<font color = "blue">            55x - 7 = 6x + 6</font>

Now get rid of the -7 on the left by adding 
its opposite +7 to both sides of the equation:

<font color = "blue">            55x - 7 = 6x + 6
                + 7      + 7
          --------------------
            55x     = 6x + 13</font>

Close up the gap:

<font color = "blue">                55x = 6x + 13</font>

Now get rid of the 6x on the right by adding 
its opposite -6x to both sides of the equation:

<font color = "blue">                55x = 6x + 13
               - 6x  -6x 
             ------------------
                49x =      13</font>

Close up the gap

<font color = "blue">                49x = 13</font>

Get rid of the 49 coefficient by dividing both sides
by 49

<font color = "blue">                49x     13</font>
<font color = "blue">               ----- = ----</font>
<font color = "blue">                 49     49</font>

Cancel the 49's on the left

<font color = "blue">                 1  
<font color = "blue">                <s>49</s>x     13</font>
<font color = "blue">               ----- = ----</font>
<font color = "blue">                 <s>49</s>     49</font>
<font color = "blue">                  1</font>

<font color = "blue">                        13</font>
<font color = "blue">                   x = ----</font>
<font color = "blue">                        49</font>
<font color = "black">
That's the answer: <font color = "blue">x = 13/49</font>, thirteen forty-ninths.

Edwin</pre></font></b>