Question

Easy question.

Simplify (Write each expression without the absolute value symbol.

|x / 3| if x = 0

I know this question is simple, I just need the steps on how you do it.

Answer 1

Answer: x/3

Explanation:

The absolute value equation can be written piecewise like this

`|x| = \begin{cases}x , \ \text{ if } x \ge 0\\-x , \ \text{ if } x < 0\end{cases}`

That is the same as saying

• If
  `x \ge 0`, then
  `|x| = x`
• If
  `x < 0`, then
  `|x| = -x`

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,
`\left|(x)/(3)\right| = (x)/(3) , \text{ when } x = 0`

I think your teacher wants you to avoid replacing x with 0. Though it's probably better to ask just to make sure.