Question

$4 < |x | > 2$
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Answer 1

The above expression is an inequality .

An equality is an expression which is represented by equal to (=) sign .

An inequality is an expression which has relations but not represented by equal to sign .

They are either shown by "more than equal to" or "less than equal to" signs .

Here it is given :

4 < |x| > 2

The above inequality can be written as :

⇒ 2 < 4 < |x|

The sign || represents that the number is converted to positive if negative .

Hence |x| > 4

x can be any number excluding { - 4, - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 , 4 }

The value of x hence starts from - 5 and 5 and then it keeps increasing / decreasing as the case may be .

Range of x :

x ∈ { - ∞ ..... - 5 , 5 ..... ∞ }

This is the required value range of x .

Answer 2

Answer:

-The expression given(4<|x|>2)is of the inequality

-A inequality is the expression which has relation but not represented by (=) sign .They are represented by more than equal to(<) or less than equal (>) to sign or sometimes both.

Now plz refer to the attachment for answer here.