SOLUTION: {{{abs(3x + 1) + abs(3 - 2x) = 11}}} {{{x = "?"}}}

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Question 258767:

Found 3 solutions by Fombitz, richwmiller, Edwin McCravy:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
Break up the number line into 3 distinct regions using the absolute value arguments.
3x+1=0
x=-1/3
When ,
When ,
.
.
.
3-2x=0
3=2x
x=3/2
When ,
When ,
.
.
.
Here are the 3 regions.
(,)




.
.
.
(,)



Not in the valid region, no solution.
.
.
.
(,)





.
.
.
Two solutions: x=-9/5 and x=13/5.
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
| 3x + 1 | + | 3 - 2x | = 11
(3x+1)+(3-2x)=11
x+4=11
x=7
I haven't dealt with absolute values in awhile .
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!



We have to solve these 4 cases

Case 1:   
Case 2:   
Case 3:   
Case 4:   

and check each in the original to see if it is a
solution or whether it is extraneous.   

Case 1:  






Check in original:








That does not check. so 7 is extraneous.

Case 2:  








Check in original:










That checks, so  is a solution.

Case 3:  







Check in original:










That checks so  is a solution.

Case 4:  







Check in original:








That does not check, so  is extraneous.

There are two solutions:

 and 

Edwin
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