Absolute Property Solutions

Basically absolute values mean a value without considering its sign. Here we are going to find the solutions of absolute properties. If we are having any number x mean absolute value of x is denoted like |x| and its value is +x. Likewise for |-x| = x. Here we are going to learn the properties of the absolute value and its solutions. If we know the properties of the absolute value it is easy to do the operations on the absolute values.

Absolute Property Solutions:

The first property is non negative property.

Absolute property solutions - Non negativity property:

Absolute value of the numbers is always greater than 0. if we are having a negative number its absolute value is a positive number.

Example:

What is the absolute value of the number -1.2?

Solution:

The given number is -1.2

We have to find the absolute value of the number -1.2

So |-1.2| = +1

So always |x| > 0

Absolute property solutions - Positive definiteness:

The second property is positive definiteness.

The absolute value of the number 0 is always 0. If |x| = 0 then x = 0 (always)

Example:

What is the absolute value of 0?

Solution:

Basically an absolute value is having two values. But for 0 the absolute value is |0| = 0

Absolute property solutions - Multiplicative property:

Multiplication of any two given absolute values equals to the individual absolute value multiplication.

|x y | = |x| |y|

Example:

|-5 x 3| = |-15| = + 15

|-5| x |3| = +5 x +3 = + 15

So both the values are same.

More Absolute Property Solutions:

Absolute property solutions - Subtraction addition property:

Addition of any two given absolute values is always less than the value of its individual addition.

|x + y| ≤ |x| + |y|

Example:

|4 + -3| = |1| = 1

|4| + |-3| = 4 + 3 = 7

1 < 7

Absolute property solutions - Symmetry property:

Symmetry property mean |-x| = |x|

Absolute value of the –x and absolute value of x is always same.

Example:

|-4| = |4| = +4

Absolute property solutions - Identity of indiscernible property:

The difference of any two absolute values of the number is 0 then these two absolute values are same.

|x - y| = 0 then x = y

Example:

Find the absolute value of |5 – (-5)|

Solution:

Absolute value of |5| = +5

Absolute value of |-5| = +5

So |5 – (-5)| = 0

Absolute property solutions - Preservation of division:

The division of any two absolute values and its individual absolute value division are equal.

|x / y | = |x| / |y| (where y ≠0)