The discussion revolves around solving the absolute value equation |x-4|*x - x = 0. Participants are exploring the implications of the absolute value function and the conditions under which they can manipulate the equation.
Participants are actively engaging with the problem, sharing various approaches to factor the equation and questioning assumptions about the values of x. There is a recognition of multiple potential solutions, but no explicit consensus on the final values has been reached.
There is an ongoing discussion about the inclusion of zero in the set of real numbers and its impact on the solution process. Some participants express confusion about the steps needed to arrive at the final solutions.
Science4ver said:Homework Statement
I have an abs-function |x-4|*x -x = 0
which I need to solve.
The Attempt at a Solution
Do I need to re-arrange so I get
|x-4| = x/x = 1
thus we have x-4 = -1 or x-4 = 1.
Hence x = 3 or x = 5 ?
Dick said:You unwisely divided by x. You can only do that if x is nonzero. You are missing a possible value for x.
Science4ver said:well in the assigment x belongs to R.
But how do I obtain the final of x? I am lost here.
mtayab1994 said:And doesn't R contain 0?
Science4ver said:it most certainly does, but what do I do with the equation to obtain the final and third solution?
Dick said:The cleanest way is to factor it into x*(|x-4|-1)=0. How can the product of two numbers be zero?
mtayab1994 said:split x*(l x-4 l -1)=0 into two equations. That should help you even more.
Science4ver said:I know then x is either zero or x is found by solving |x-4|-1 = 0
cool, thanks !
mtayab1994 said:Great ! And what are the values?
Why the question mark? (In both this and your original post.)Science4ver said:x = 0 or x = 3 og x = 5?
HallsofIvy said:Why the question mark? (In both this and your original post.)
What do you get if you put one of those numbers into the original equation?