SOLUTION: Please help me to answer this question. Solve {{{(x)abs(5x-1) = (2x-4)}}}

Algebra ->  Absolute-value -> SOLUTION: Please help me to answer this question. Solve {{{(x)abs(5x-1) = (2x-4)}}}      Log On


   

Question 1049350: Please help me to answer this question. Solve %28x%29abs%285x-1%29+=+%282x-4%29
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the definition of the absolute value function to break up the function into two functions.
1.x%285x-1%29=2x-4 when 5x-1%3E=0
2.-x%285x-1%29=2x-4 when 5x-1%3C0
So then,
Using eq. 1,
5x%5E2-x=2x-4
5x%5E2-3x%2B4=0
No real solutions.
Using eq. 2,
-5x%5E2%2Bx=2x-4
-5x%5E2-x%2B4=0
5x%5E2%2Bx-4=0
%28x%2B1%29%285x-4%29=0
Two solutions:
x%2B1=0
x=-1
and
5x-4=0
5x=4
x=4%2F5
However we have to check our original condition,
5x-1%3C0
5x%3C1
x%3C1%2F5
So then only x=-1 would be a solution.