Section 2.8 Linear Inequalities 185 Interval Notation To understand interval notation, first think of a number line extending infinitely far to the right and infinitely far to the left. Sometimes we use the infinity symbol, , , or negative infinity symbol, to label the far right and far left ends of the number line (Figure 2-10). 0 To express the solution set of an inequality in interval notation, sketch the graph first. Then use the endpoints to define the interval. Inequality Graph Interval Notation x 2 32, 2 The graph of the solution set begins at 2 and extends infinitely far to the right. The corresponding interval notation begins at 2 and extends to . Notice that a square bracket is used at 2 for both the graph and the interval notation. A parenthesis is always used at and for , because there is no endpoint. x 2 ( 1 0 1 2 3 4 5 6 4 3 2 2 , 6 5 Using Interval Notation • The endpoints used in interval notation are always written from left to right. That is, the smaller number is written first, followed by a comma, followed by the larger number. • A parenthesis, ( or ), indicates that an endpoint is excluded from the set. • A square bracket, or , indicates that an endpoint is included in the set. • A parenthesis, ( or ), is always used with and , respectively. In Table 2-1, we present examples of eight different scenarios for interval notation and the corresponding graph. Interval Interval Notation Graph Notation Graph (a, ( ) a, ) a a ( (, a) (, a a a ( ( (a, b) a, b a b a b ( (a, b a, b) ( a b a b Table 2-1 Figure 2-10 Concept Connections 5. Translate the phrase below to set-builder notation. The set of all b such that b is greater than or equal to 20. 6. Translate the phrase below to interval notation. The set of all x such that x is less than 30. Answers 5. {b 0 b20} 6. (,30)
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