Question 50865
<pre><font size = 3><b>students in Japan go to school an average of <font color = "red">232+3x</font> days, while students in the
U.S. go to school an average of <font color = "blue">184+4x</font> days. How many more days, on average
does a japanese student attend school each year?

First think how you would do if it had read numbers instead of algebraic
expressions.

Suppose first that it had read this way, as in the second or third grade:

Students in Japan go to school an average of <font color = "red">250</font> days, while students in the
U.S. go to school an average of <font color = "blue">150</font> days. How many more days, on average does a
japanese student attend school each year?

In the 2nd grade you would go:

<font color = "red">250</font> - <font color = "blue">150</font> 

and get <font color = "darkgreen">100</font> days.

So in algebra you go: 

<font color = "red">(232+3x)</font> - <font color = "blue">(184+4x)</font> and get <font color = "darkgreen">100</font> days.

Now you remove the parentheses by sticking a factor <font color = "indigo">1</font> just before them:

<font color = "indigo">1</font>(232+3x) - <font color = "indigo">1</font>(184+4x)

Then we remove the parentheses by the distributive principle:

232 + 3x - 184 - 4x

Then combine like terms

   48 - x 

Edwin</pre>