Absolute value

by **anand_nesan** Mon Oct 06, 2008 2:19 pm

One of the Manhattan GMAT practice test questions (Question name - "Work Your Abs") had this equation

3|x^2 - 4| = y - 2

The answer explanation for this equation came to the following conclusion - "absolute value expression |x^2 - 4| must be greater than or equal to 0."

How can we arrive at this conclusion? Any help is appreciated.

by **Saurav** Wed Oct 29, 2008 4:05 pm

That i think is the definition of modulus, for example anything written as | X | (where X is any number - real, integer) the value is a positive value , i.e. |X| is always a positive value.

incase X=0, then |X| =0

by **JonathanSchneider** Thu Nov 13, 2008 2:16 am

Saurav, you are absolutely correct.

An absolute value (that's what those bars represent) cannot be negative.

by **nadair** Thu Nov 20, 2008 2:06 am

Keep in mind that the absolute value of a number is merely its distance from zero.

Example: |-3| = 3

-3 -2 -1 0 1 2 3
|------|------|------|------|------|------|

<-----3 Units------>

by **nadair** Thu Nov 20, 2008 2:07 am

Sorry, the numbers on the number line got jumbled together after posting. They should have appeared above each tick mark.

by **JonathanSchneider** Wed Dec 10, 2008 9:26 pm

Exactly. I'm a big fan of drawing the number line whenever I see absolute value bars.