# Rewrite the expression without using the absolute value symbol.

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• Mar 2nd 2012, 10:27 AM
joshuaa
Rewrite the expression without using the absolute value symbol.
Could you please help me solve this absolute value with explanation?

|4 - pi|

(Doh)
• Mar 2nd 2012, 10:31 AM
Plato
Re: Rewrite the expression without using the absolute value symbol.
Quote:

Originally Posted by joshuaa
Could you please help me solve this absolute value with explanation?
|4 - pi|

$\displaystyle 4>\pi$ so $\displaystyle 4-\pi>0$ thus $\displaystyle |4-\pi|=~?$
• Mar 2nd 2012, 10:40 AM
joshuaa
Re: Rewrite the expression without using the absolute value symbol.
I am not good in math, so I can not figure out the answer. Your explanation is good, but you need to give me the final answer.
• Mar 2nd 2012, 10:51 AM
Plato
Re: Rewrite the expression without using the absolute value symbol.
Quote:

Originally Posted by joshuaa
I am not good in math, so I can not figure out the answer. Your explanation is good, but you need to give me the final answer.

If $\displaystyle a>0$ then $\displaystyle |a|=a~.$
• Mar 2nd 2012, 10:52 AM
joshuaa
Re: Rewrite the expression without using the absolute value symbol.
After a very long thinking, now I get it. The answer would be just 4 - pi. And if if we reverse the question like this |pi - 4|, pi - 4 will be less than zero. Therefore, the answer will be -(pi - 4) = 4 - pi.

What if want the answer, but we do not know the value of X, like this?
|4 - X| = ?
• Mar 2nd 2012, 11:19 AM
Plato
Re: Rewrite the expression without using the absolute value symbol.
Quote:

Originally Posted by joshuaa
What if want the answer, but we do not know the value of X, like this? |4 - X| = ?

This may surprise you, but $\displaystyle |4-x|=|x-4|$.

So $\displaystyle \left| {x - 4} \right| = \left\{ {\begin{array}{rl} {x - 4,} & {x \ge 4} \\ {4 - x,} & {x < 4} \\\end{array}} \right.$
• Mar 2nd 2012, 11:36 AM
joshuaa
Re: Rewrite the expression without using the absolute value symbol.
I am not going to go deeper this time, but I have really understood what I was wondering about. Thank you very much, and I hope that we will be meeting in other questions(Hi)