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The absolute value is always a positive number except for zero, as zero is neither positive or negative. Absolute value refers to the distance of a number from zero, regardless of direction. The distance is always positive, as absolute value of a number cannot be negative. Use this term to refer to the distance of a point or number from the origin (zero) of a number line.

### Examples

The symbol to show the absolute value is two vertical lines: | -5 | = 5. This means that the absolute value of "-5" is "5" because "-5" is five units away from zero. Put another way:

|5| shows that the absolute value of 5 is 5.

|-5| shows that the absolute value of -5 is 5

### Sample Problems

Find the absolute value for the following problem.

|3x| = 9

To solve this problem, divide each side by "3," yielding:

x = 3

The absolute value of "3" is either "-3" or "3" because the number "3" or "-3" is three spaces from zero. So, the answer is:

(3, −3)

Or, try the following problem.

|−3r| = 9

To find the answer, divide each side by "3" to isolate the variable "r," yielding:

|−r| = 3

As with the previous problem, "r" can be either "3" or "-3" because three is three spaces or units from zero. So, the answer is:

(−3, 3)