# MandysNotes

## Absolute Value Example Problems, Diagram

20 March 2010 By
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Absolute value is the distance on a number line between any given point and zero.

Therefore, because distance is always POSITIVE (you cannot have a negative distance), absolute value is also always POSITIVE.

For example, if you have |x| = 2

This means that x = -2 or 2

WHY?  Because distance is always POSITIVE.

Therefore, remember: Any variable in brackets could have TWO values, one positive and one negative.

Example problem:

If |x| - 3 = 0, what is x?

Answer:

Clearly, if x = 3, then |x| - 3 = 0.

However, if x = -3, then |x| = | -3| = 3, and once again,

|x| - 3 = 0.

Therefore x, in this equation can be either 3, or -3.

Example problem:

If |x| - 2 = 7, what is |x|?

First we add two to both sides to obtain:

|x| = 9.

Therefore x could be either 9, or -9.

If we are given another condition, such as:

|x| -2 = 7,

and

x < 0,

then we know that the answer must be x = -9.

Read 6105 times Last modified on Thursday, 13 February 2014 21:53

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