Answer: x/3
Explanation:
The absolute value equation can be written piecewise like this
[tex]|x| = \begin{cases}x , \ \text{ if } x \ge 0\\-x , \ \text{ if } x < 0\end{cases}[/tex]
That is the same as saying
- If [tex]x \ge 0[/tex], then [tex]|x| = x[/tex]
- If [tex]x < 0[/tex], then [tex]|x| = -x[/tex]
Let's have y = x/3
If x = 0, then y = 0/3 = 0
So to compute |y|, we'll use the first rule mentioned above.
Therefore, [tex]\left|\frac{x}{3}\right| = \frac{x}{3} , \text{ when } x = 0[/tex]
I think your teacher wants you to avoid replacing x with 0. Though it's probably better to ask just to make sure.
