# Homework Help: Solving an absolut-valued function

1. Dec 12, 2011

### Science4ver

1. The problem statement, all variables and given/known data

I have an abs-function |x-4|*x -x = 0

which I need to solve.

3. 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 ?

2. Dec 12, 2011

### Dick

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

3. Dec 12, 2011

### Science4ver

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 ?

4. Dec 12, 2011

### mtayab1994

And doesn't R contain 0?

5. Dec 12, 2011

### Science4ver

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

6. Dec 12, 2011

### Dick

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

7. Dec 12, 2011

### mtayab1994

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

8. Dec 12, 2011

### Science4ver

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

cool, thanks !

9. Dec 12, 2011

### mtayab1994

Great !! And what are the values?

10. Dec 12, 2011

### Science4ver

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

11. Dec 12, 2011

### mtayab1994

Nice job!

12. Dec 12, 2011

### HallsofIvy

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?

13. Dec 13, 2011

### Science4ver

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