94.5k views
23 votes
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.

1 Answer

2 votes

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.

User Akhil Rao
by
7.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.