Good at Algebra?? Please help, and fast!!!! 10 points!

an interval which is written as (x,y) refers to all numbers between x and y i.e. the intervals include all numbers greater than x but less than y.
the type of bracket used : ( ) or [] , will determine whether to include x and y in the interval or not.
i have explained that below :

if a interval is given as (x,y) it is an open interval i.e it includes all numbers between x and y but not x and y.

if a interval is given as [x,y] it is a closed interval i.e it includes all numbers between x and y including x and y.

if a interval is given as [x,y) ,it includes all numbers between x and y including x but not y.

if a interval is given as (x,y] , it includes all numbers between x and y including y but not x.


note that :

in interval (-x, infinity ) ,
since x is negative , the interval will contain all numbers between -x and 0 and all positive numbers.



( note that since it is an open interval, -x will not be included in the interval.
you can assume infinity as just another variable. don't bother about it . it just means all positive numbers.
take care to apply the concept of open and closed intervals in each case)


similarly, in interval (x, infinity ):
since x is positive the interval will contain all positive numbers greater than x but not x.


similarly, in interval (- infinity,x ):
since x is positive ,the interval will contain all negative integers and all integers between 0 and x but not x, since it is an open interval

similarly in interval ( - infinity, -x ):
since x is negative the interval will contain all negative numbers less than -x but not -x.

the interval will ( - infinity , infinity ) will contain all negative integers, 0 , and all positive integers.
also : ( - infinity , infinity ) and [- infinity , infinity ] will mean the same thing at this level.
the type of bracket used in accordance with infinity wouldn't matter.