How do you express intervals as inequalities such as [-2,9]?

1 Answer
Feb 20, 2017

Answer:

#[-2,9]# is written as the inequality #-2<=x<=9#

Explanation:

The expression #[-2,9]# in interval form means that

the concerned variable, say #x# has a lower limit of #-2# and including #-2#, as we have square brackets but had we parentheses i.e. '#(#', this means that #-2# is not included.

In other words #x>=-2# as value of #x# is not less than #-2#.

Further, as the interval has an upper limit of #9#, again including #9#, as we have square brackets but had we parentheses i.e. '#(#', this means that #9# is not included.

In other words #x<=9# as value of #x# is not greater than #-2#.

The two limits can then be combined as #-2<=x<=9#

Note that had it be #(-2,9)#,

the result would have been #-2 < x < 9#.

#(-2,9]# as #-2 < x <= 9#

and #[-2,9)# as #-2 <= x < 9#