Question 562644: |5x-1|+7=3x
Answer by issacodegard(60)   (Show Source):
You can put this solution on YOUR website! I'll prove that there is no solution.
Suppose that there is a solution x.
Then suppose 5x-1>=0. Then x>=1/5. And we have,
|5x-1|+7=3x
5x-1+7=3x
2x=-6
x=-3
But, this is not possible since x>=1/5.
So, suppose 5x-1<=0. Then x<=1/5. We have,
|5x-1|+7=3x
-(5x-1)+7=3x
-5x+1+7=3x
8x=8
x=1
But, this is not possible since x<=1/5.
So, by contradiction, there is no solution.
Looking at the graphs of the left hand and right hand sides of the equation will show that they don't intersect.
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