Question 68204
<pre><font size = 5><b>Translate the following statement into an algebraic 
equation. Let x represent the number.
 
6 times a number is 14 more than that number.

After each step, I'll color some of the words red, then
I'll replace them. Then I'll copy it over with some new
words colored red.

6 times <font color = "red">a number</font> is 14 more than that number.

Replace the words "<font color = "red">a number</font>" by <font color = "red">x</font>. Now we have:

6 times <font color = "red">x</font> is 14 more than that number.

6 times x is 14 more than <font color = "red">that number</font>.

Replace the word "<font color = "red">that number</font>" also by <font color = "red">x</font>. Now we have:

6 times x is 14 more than <font color = "red">x</font>.

<font color = "red">6 times x</font> is 14 more than x.

Replace the words "<font color = "red">6 times x</font>" by "<font color = "red">6x</font>". Now we have

<font color = "red">6x</font> is 14 more than x.

6x is <font color = "red">14 more than x.</font>

Now we need to replace the words "<font color = "red">14 more than x</font>" 
by something.
This is a little harder but not much.  To get 14 more 
than x, we start with x, so we write x first, then we 
want to make it 14 more by adding ("plussing") 14 
onto it. So we want to replace "<font color = "red">14 more than x</font>" by 
"<font color = "red">x + 14</font>".  [Caution: <i>we want to translate exactly,
so we should write "<font color = "red">x + 14</font> and not "14 + x", because
we are starting with x and making it more.  We are 
not starting with 14.</i>)  So we now have:

6x is <font color = "red">x + 14</font>

6x <font color = "red">is</font> x + 14

Finally we replace the word "<font color = "red">is</font>" by "<font color = "red"> = </font>"

6x <font color = "red">=</font> x + 14

6x = x + 14

That's the algebraic equation!

Edwin</pre>