Inequalities - Types of Brackets
Graphing Solution Sets for Inequalities Part Two
You may be asked to give your solution set using brackets instead of the inequality symbols.
If you are including the number on the left or the right you use [ ]
If you are not including the number on the left or right you use ( )
If you are using infinity, you write for example:
= "x is greater than 7"
The parenthesises here are saying that x can be any number greater than 7 but not 7 itself.
= "x is less than 7"
The parenthesises here are saying that x can be any number less than 7 but not 7 itself
[7, infinity) = "X can be equal to 7 or any number greater than 7"
The square bracket here is saying that "x can be equal to 7," the parenthesis next to the
infinity are saying that "or x can also be any number greater than 7."
( - infinity, 7] for x is less than or equal to 7 = "X can be equal to 7 or any number less than 7"
The square bracket here is saying that "x can be equal to 7," the parenthesis next to the
infinity are saying that "or x can also be any number less than 7."
NOTE: You always use a parenthesis () for infinity.
Why?
Think about it before reading answer below.
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The square bracket means that x can be equal to that number.
But, you cannot say "x equals infinity." (Hence, we use the parenthesises.)
In mathematics, that statement does not make sense.
X can't be infinity because infinity is "a number greater than any assignable quantity or countable number (Oxford Dictionary of English)." It is more an idea than an actual number, thus we cannot say that x is equal to "it" since "it" is inconceivable.
Use the activity below to help you practice interpreting the meaning of the solution sets written using brackets.
-Ms. Duffy