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INTERVAL NOTATION
When an equation is solved, the solution set generally involves a finite set of numbers.
For example, the solution to the
equation 2
1
7
x
+ =
is the number x
=
3 , while the solutions to the equation x
2
1
10
+ =
are x
= ±
3 .
When we solve an
inequality, however, the solution is usually a “connected” set of real numbers, called an interval.
Using the above examples,
the solutions to the inequality 2
1
7
x
+ >
are all numbers greater than 3, and the solutions to the inequality x
2
1
10
+ ≤
are all
numbers between or equal to
±
3 .
Interval notation provides us with some useful mathematical shorthand for representing
intervals of numbers.
Parentheses ( ) are used whenever the endpoint of an interval is not included in the solution set, and brackets [ ] are used
whenever the endpoint is included.
The symbols for positive and negative infinity,
±∞
, are used whenever an interval has
only one endpoint.
Brackets are never used on the infinite end of an interval involving the

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