What does this symbol mean in math |number| ?

[Wile E.]

In pre-Windows MSDOS computers, the | symbol used alone was called a pipeline and, at the time, had no place in mathematics. In Twitter, it's called a hashtag.

Used in pairs with an algebraic or numberic expression inside them, they are called absolute value symbols. Basically, the ultimate value of the expression has neither a positive nor negative value, it just has a value. Essentially, the expression itself can be positive or negative, resulting in two possible solutions. Possible because one solution may be extraneous.

To use your example,

|3x - 7| = 8
± (3x - 7) = 8

First Possible Solution:

+ (3x - 7) = 8
3x - 7 = 8
3x = 8 + 7
3x = 15
x = 15 / 3
x = 5

Second Possible Solution:

- (3x - 7) = 8
- 3x + 7 = 8
- 3x = 8 - 7
- 3x = 1
x = - 1/3

Testing Each Possible Solution,

If x = 5,

|3(5) - 7) = 8
|15 - 7|= 8
|8| = 8

If x = - 1/3,

|3(- 1/3) - 7| = 8
|- 1 - 7| = 8
|- 8| = 8

x = 5 and x = - 1/3 are both valid solutions.
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A real world application of the absolute value is in calculating the hypotenuse of a right triangle given the two sides. As you know, the hypotenuse is the square root of the sum of the squares of the sides. Normally, square rooting will return a positive/negative value, but the hypotenuse can be neither positive nor negative.
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