x is the set of all intergers n that satisfy the inequality

\"x is the set of all intergers n that satisfy the inequality 2<or= to the absolute value of n, which is < or = to 5. Is THE ABSOLUTE VALUE OF THE GREATEST INTERGER IN X GREATER or is the absolute value of the least interger in x greater?

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Solution

\"x is the set of all intergers n that satisfy the inequality 2<or= to the absolute value of n, which is < or = to 5. Is 2<= equal to <=5, or are one of them greater?\"

Solution :

2 <= |n| <= 5

Lets take 2 <= |n|....
|n| >= 2
n >= 2 or n <= -2
(-inf , -2] U [2 , inf) ---> Solution for |n| >= 2

Lets now take |n| <= 5
n <= 5 and n >= -5
[-5 , 5] --> solution for |n| <= 5

We must now ocmbine both those intervals and take only the parts that are common to both....

The part common to
(-inf , -2] U [2 , inf)
AND
[-5 , 5]

is [-5 , -2] U [2 , 5]

So, our answer is simply :

x = [-5 , -2] U [2 , 5]

THE ABSOLUTE VALUE OF THE GREATEST INTERGER IN X is |5| = 5

absolute value of the least interger in x is | -5| = 5

So, the absolute value of the greatest integer in x is equal to the absolute value of the least integer in x