SOLUTION: Please help me solve this problem {{{abs(f+3)=2f+4}}}

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Question 153627This question is from textbook McDougal Littell Algebra2
: Please help me solve this problem abs%28f%2B3%29=2f%2B4 This question is from textbook McDougal Littell Algebra2

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me solve this problem abs%28f%2B3%29=2f%2B4

There are two cases to consider: 

Case 1:  abs%28f%2B3%29=2f%2B4 where f%2B3%3E=0

Case 2:  abs%28f%2B3%29=2f%2B4 where f%2B3%3C0

Let's do case 1 first:

abs%28f%2B3%29=2f%2B4 where f%2B3%3E=0

Then to get rid of the absolute value bars, we can just drop
them because the absolute value of any positive number
is just that positive number and the absolute value of 0
is also just that number, 0.  So

abs%28f%2B3%29=2f%2B4  becomes

f%2B3=2f%2B4

Solve that and get f=-1

So that is one solution, for when we check it,

abs%28f%2B3%29=2f%2B4
abs%28-1%2B3%29=2%28-1%29%2B4
abs%282%29=-2%2B4
2=2


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Now let's do case 2:

abs%28f%2B3%29=2f%2B4 where f%2B3%3C0

Here f%2B3 is a negative number. Therefore to get 
rid of the absolute value bars, we can make the negative 
number f%2B3 positive by multiplying it by -1.  So

abs%28f%2B3%29=2f%2B4  becomes

-1%28f%2B3%29=2f%2B4

Solve that and get f=-7%2F3

However that is not a solution, for when we check it,

abs%28f%2B3%29=2f%2B4
abs%28-7%2F3%2B3%29=2%28-7%2F3%29%2B4
abs%28-7%2F3%2B9%2F3%29=-14%2F3%2B4
abs%282%2F3%29=-14%2F3%2B12%2F3
abs%282%2F3%29=-2%2F3
2%2F3=-2%2F3

So there is just one solution, f=-1

Edwin