What is absolute value?

What is absolute value?
Absolute value of number is defined asthe difference between it and zero and is denoted by symbol of |x| or sometime we can use abs(x). Absolute valueismost commonly used by mathematicians and scientists as a tool which is used to separate magnitude and direction when only magnitude matters. Absolute value is positive. The absolute value of a real number is the difference between that real number and zero

If x is the real number then the absolute value for real number |x| = x, when it is positive. |x| = -X, when x is not positive. The absolute value is the distance of x from 0.
The equation for absolute value is,
K = |x-b| ------------- (1)
If x-b is positive
Then k = x - b
X = b + k   ------------- (2)
If x-b is negative
-k = x - b
X = b – k ---------------- (3)
Finding the absolute values.
Example: | x-5 | = 7
From equations 2 and 3 the absolute values are
| x-5 | = 7 | x-5| = -7
X = 7 + 5 x = -7 + 5
X = 12 x = -2
So the absolute values are {12, -2}

Definition for absolute value

The absolute value of a number measures its distance to the origin/zero on the real number line. From above the figure x is 5 units away from the zero. The absolute value is always positive, so it can change the sign of the negative number in to positive number. But the absolute value of zero has no sign, since it is equal to its absolute value.

Absolute value equations:
Isolate the absolute value expression to solve absolute value equations. The expression is called as k. Then write both the equations in which the expression provided within the absolute value symbol is one of the two expressions.  Write the first equation k should be equal to the expression inside the absolute value symbol, and then write the other equation should be equal to –k. Then we get the set of solution obtaining the solution for the equations.

Example: | 2x+12 | = 4x
| x – b | = k
From above equation 2 and 3
| x – b | = k | x – b | = - k
2x + 12 = 4x 2x + 12 = -4x
X = 6 x = -2
So the solution of equation is {-2, 6}

Absolute value in algebra
Absolute value is defined as; it is functions which measure the size of the element as a field or integral domine (D).
|x| = 0
|x| = 0 if and only if x =0
|xy| = |x||y|
|x+y| = |x| + |y|

Example: |1|  = 1
  |-1| = 1