Expert: Abe Mantell - 5/27/2009

Question
Hello!
Could you please help me with these problems? I have an idea of how to do these, but am not entirely sure that I am right. Any sort of help will be very much appreciated!

Thanks so very much!
Amanda
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1.) Solve for x: | x + 2 | = 8
 6 only  
 -6, 10  
 No solution  
 6, -10  

2.) Solve for x: | -3x - 6 | = 21
 -9 only  
 -9, 5  
 9, -5  
 No solution  

3.) Solve for x: | -2x - 3 | = -5
 1 only  
 1, -4  
 No solution  
 -1, 4  

4.) Solve | x - 4 | = | 5 - 2x |
 1, 3  
 1 only  
 3, -3  
 -1, -3  

5.) Solve for x: | -2x + 3 | = | x - 15 |
 6, -6  
 6, -12  
 -6, 12  
 -6 only

6.) Solve for x: | 2x - 4 | + 3 = 5
 3 only  
 -3 only  
 3, 1  
 3, -2  

7.) Solve for x: | 5 - x | = | -x + 3 |
 No solution  
 0, 4  
 -1, 1  
 4 only  

8.) Solve for x: | x/3 - 4 | = 2/3
 10, 14  
 6, 2  
 -10, -14  
 -6, -2

9.) Solve for x: | x/6 + 5 | + 1/3 = 3/4
 0, -5  
 -25, -30  
 -55/2, -65/2  
 0, -9  

Answer
Hello Amanda,

Wow, you have many questions there...looks like a HW list!

How about I do 3 of them so you get the idea.
(Of course, you could simply just check each answer, but here is
how you do them...)

1.) Solve for x: | x + 2 | = 8
-- Either x+2=8 or -(x+2)=8
-- (since the absolute value will "get rid of" the negative sign...)
-- Thus, either x=6 or x=-10

4.) Solve | x - 4 | = | 5 - 2x |
-- Either x-4=5-2x or -(x-4)=5-2x
-- (the other two cases would be equivalent to one of these)
-- Thus, 3x=9 or -x+4=5-2x ==> x=3 or x=1

9.) Solve for x: | x/6 + 5 | + 1/3 = 3/4
-- | x/6 + 5 | = 3/4 - 1/3
==> Either x/6 + 5 = 5/12 or -(x/6 + 5) = 5/12
==> x/6 = 5/12 - 5 or -x/6 - 5 = 5/12
==> x=-55/2 or x=-65/2

I hope this enables you to finish the rest of them...OK?

Abe