An absolute value of |x| {modulus of x} is the value of a real number x. The given equation is not true.
An absolute value of |x| {modulus of x} is the value of a real number x, the value we get is always a non-negative number, for example, |-5| will give 5, and also, |5| will give 5 as well.
A hypothesis is a speculative conclusion or assertion that is made without proof. Now, to prove that the given equation is not true substitute the value of both the variables as -1. Therefore,
x = y = -1
Substitute the value on the left side of the equation,
|x - y|
= |-1 - (-1)|
= |-1 + 1|
= |0|
= 0
Substitute the value on the right side of the equation,
|x| - |y|
= |-1| - |-1|
= 1 + 1
= 2
Since the left and the right side of the equation is not satisfied, therefore, it can be concluded that the given equation is not true.
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