jameslee2798
Answered

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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.

Sagot :

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.

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