Solving an absolut-valued function

[Science4ver]

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]

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 ?

You unwisely divided by x. You can only do that if x is nonzero. You are missing a possible value for x.

 

[Science4ver]

You unwisely divided by x. You can only do that if x is nonzero. You are missing a possible value for x.

well in the assigment x belongs to R.

But how do I obtain the final value of x? I am lost here. Any way to remove the abs value ?

 

[mtayab1994]

well in the assigment x belongs to R.

But how do I obtain the final of x? I am lost here.

And doesn't R contain 0?

 

[Science4ver]

And doesn't R contain 0?

it most certainly does, but what do I do with the equation to obtain the final and third solution?

 

[Dick]

it most certainly does, but what do I do with the equation to obtain the final and third solution?

The cleanest way is to factor it into x*(|x-4|-1)=0. How can the product of two numbers be zero?

 

[mtayab1994]

The cleanest way is to factor it into x*(|x-4|-1)=0. How can the product of two numbers be zero?

split x*(l x-4 l -1)=0 into two equations. That should help you even more.

 

[Science4ver]

split x*(l x-4 l -1)=0 into two equations. That should help you even more.

I know then x is either zero or x is found by solving |x-4|-1 = 0

cool, thanks !

 

[mtayab1994]

I know then x is either zero or x is found by solving |x-4|-1 = 0

cool, thanks !

Great ! And what are the values?

 

[Science4ver]

Great ! And what are the values?

x = 0 or x = 3 og x = 5?

 

[mtayab1994]

Nice job!

 

[HallsofIvy]

x = 0 or x = 3 og x = 5?

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?

 

[Science4ver]

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?

They mean nothing. Simply placed them in the wrong place.