166 Chapter 2 Linear Equations and Inequalities The following inequalities are linear equalities in one variable. 2x 3 6 11 4z 3 7 0 a 4 5.2y 10.4 The number line is a useful tool to visualize the solution set of an equation or inequality. For example, the solution set to the equation x 2 is {2} and may be graphed as a single point on the number line. The solution set to an inequality is the set of real numbers that make the inequality a true statement. For example, the solution set to the inequality is all real numbers 2 or greater. Because the solution set has an infinite number of values,we cannot list all of the individual solutions. However, we can graph the solution set on the number line. The square bracket symbol, , is used on the graph to indicate that the point is included in the solution set. By convention, square brackets, either or , are used to include a point on a number line. Parentheses, ( or ), are used to exclude a point on a number line. The solution set of the inequality includes the real numbers greater than 2 but not including 2. Therefore, a ( symbol is used on the graph to indicate that is not included. In Example 1, we demonstrate how to graph linear inequalities. To graph an inequality means that we graph its solution set.That is, we graph all of the values on the number line that make the inequality true. Graphing Linear Inequalities Example 1 Graph the solution sets. 7 3 a. b. c. Solution: a. The solution set is the set of all real numbers strictly greater than Therefore, we graph the region on the number line to the right of Because is not included in the solution set, we use the ( symbol at c . 73 b. is equivalent to 1. x 1 2 3 4 5 6 13 The solution 13 set is the set of all real numbers less than or equal to Therefore, graph the region on the number line to the left of and including 2. Use the symbol to indicate that c 2is included in the solution set. 213 . 2 6 5 4 3 2 1 0 1 13 c 213 x 1. 1. ) 6 5 4 3 2 1 0 1 2 3 4 5 6 x 7 1 c 3 7 y x 7 1 ) x 7 2 6 5 4 3 2 1 0 1 2 3 4 5 6 x 2 x 7 2 x 2 x 2 6 5 4 3 2 1 0 1 2 3 4 5 6 x 2 x 2 6 5 4 3 2 1 0 1 2 3 4 5 6
miller_beginning_intermediate_algebra_4e_ch1_3
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