Question 209593
Solve each equation. Check for extraneous solutions. 
Equation: |5x-1|+7=3x 
Here's what I did: 
|5x-1|+7=3x
-7 -7 
|5x+1|=3x-7 
5x-1=3x-7 OR 5x-1=-(3x-7)
+1 +1 

5x=3x-6 
-3x -3x 

2x=-6 
-- -- 
2 2 

x=-3 
OR
5x-1=-(3x-7)
5x-1=-3x+7
8x = 8
x = 1 
So, x=-3 or x=1. 
CHECK:
|5x-1|+7=3x
|5(-3)-1|+7=+3(-3)
|-15-1|+7=-9
|-16|+7=-9 
16+7=-9
23=9
But 23 doesn't equal 9. At first I thought it was just an exraneous solution. But then I checked the second number: 
|5x-1|+7=3x
|5(1)-1|+7=3(1)
|5-1|+7=3
|4|+7=3
4+7=3
11=3
But again, 11 doesn't equal 3.
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Your work is correct.
Both "solution" are extraneous.
---
If you graph the left side and the right side of the equation
separately, you will see that they do not intersect, i.e. they
are never equal.
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Cheers,
Stan H.
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