168 Chapter 2 Linear Equations and Inequalities 2. Set-Builder Notation and Interval Notation Graphing the solution set to an inequality is one way to define the set.Two other methods are to use set-builder notation or interval notation. Set-Builder Notation The solution to the inequality x 2 can be expressed in set-builder notation as follows: 5x 0 x 26 ⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩ ⎧⎪⎨⎪⎩ ⎧⎪⎨⎪⎩ ⎧⎨⎩ the set of all x such that x is greater than or equal to 2 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 Figure 2-10 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 ( 1 0 1 2 3 4 5 6 4 3 2 2 , 6 5 The graph of the solution set x 2 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. 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 or , respectively.
miller_beginning_intermediate_algebra_4e_ch1_3
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