Solving Absolute Value Problem | 3-x=x-3

[Polymath89]

I'm currently reviewing pre-calculus material and encountered a little problem with an absolute value expression.

|3-x|=x-3

Now the way I learned absolute value expressions was that there's a positive and a negative case. So I got:

3-x=x-3 x=3 and -(3-x)=x-3 gives 0=0. Stupid question, but isn't 0=0 in general valid for all values of x? And I don't understand how you get to the solution x≥3.

 

[mfb]

If you distinguish two different cases, you should keep in mind where those cases apply. Here, your case $3-x \leq 0$ is valid for $x \geq 3$ only.