Question

How do you solve \[|x| > 1\]?

Answer 1

Hint: Here we have to solve the given equation. The question is involved the arithmetic symbol that is greater than symbol the mod symbol. By the definition of absolute number we are determined the unknown variable. Hence we obtain the required solution for the question.

Complete step-by-step answer:
 In mathematics we have different forms of numbers namely, natural numbers which are known as counting numbers, whole numbers are the natural numbers and also include 0, integers are combination of whole numbers and negative of natural numbers, rational numbers are in the form of \[\dfrac{p}{q},q \ne 0\], irrational numbers are not rational numbers, real numbers are the combination of integers and rational numbers.
in mathematics there are arithmetic symbols
When the number “a” is less than the number “b”, it is represented as a < b. When the number “a” is greater than the number “b”, it is represented as a > b. When the number “a” is equal to the number “b”, it is represented as a = b. and so on.
The absolute value or modulus of a real number x, it is denoted as |x|, is the non-negative value of x without considering its sign.
Now consider the given question \[|x| > 1\]
Where \[|x|\] = \[+x\; for\; x>0\] and \[-x \;for\; x<0\]
By definition the modulus will take the positive value so it is written as
\[x > 1\]
Hence the value of x should be greater than 1.
Or it can be solved by the another way
Now consider the given question \[|x| > 1\]
Where \[|x|\] = \[+x\; for\; x>0\] and \[-x \;for\; x<0\]
Squaring on both sides to the given equation
\[ \Rightarrow |x{|^2} > {1^2}\]
While squaring the positive value and the negative value will becomes positive so we have
\[ \Rightarrow x > 1\]
Hence the value of x should be greater than 1.
Hence the x can take the value like 2, 3, 4 and so on.

Note: When the number or the equation contains the modulus symbol, the number or equation will take the positive value. If the negative value in the modulus symbol then it is considered as positive value itself. The squaring of the number will always be the positive value.