SOLUTION: Solve for x: /x-4/=/2x+1/

Algebra ->  Expressions -> SOLUTION: Solve for x: /x-4/=/2x+1/      Log On


   

Question 1020925: Solve for x: /x-4/=/2x+1/
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The quickest way of solving this equation is to square both sides. This will effectively take away the absolute value bars.
%28x-4%29%5E2+=+%282x%2B1%29%5E2
<==> x%5E2+-+8x+%2B16+=+4x%5E2+%2B+4x+%2B1
<==> 0+=+3x%5E2+%2B12x+-15
<==> 0+=+x%5E2+%2B4x+-5 ==> (x+5)(x-1) = 0 ==>x = highlight%28-5%29 or highlight%281%29.
Direct substitution of each value into the original equation verifies that both of them are solutions.
There is another way of solving this equation which requires the determination of the critical numbers of the equation (effectively partitioning the real number line) to eliminate the absolute value bars.