Question 470469
<font face="Times New Roman" size="+2">


I don't know how <i>you</i> would solve the problem.  I can show you how 
<i><b>I</b></i> solve it.  Then you can decide for yourself whether that is the method you will use.


First recall the definition of absolute value:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ |x|\ =\ \left\{\ \ x\text{ if }x\ \geq\ 0\cr-x\text{ if }x\ <\ \,0\right]


That means we can say that


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ |3(y\ +\ 4)|\ =\ 12]


means that


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3(y\ +\ 4)\ =\ 12]


or


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3(y\ +\ 4)\ =\ -12]


Now all that is left is to solve the two ordinary equations to get the two elements of the solution set.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
<div style="text-align:center"><a href="http://outcampaign.org/" target="_blank"><img src="http://cdn.cloudfiles.mosso.com/c116811/scarlet_A.png" border="0" alt="The Out Campaign: Scarlet Letter of Atheism" width="143" height="122" /></a></div>
</font>