SOLUTION: 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

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
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.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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.
-----------------------------------------
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.
=======================
Cheers,
Stan H.
Reply to stanbon@comcast.net
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