Section 2.8 Linear Inequalities 167 c. This inequality reads “3 is greater than y.”This is equivalent to saying, “y is less than 3.” The inequality 3 y can also be written as y 3. 3 7 y The solution set is the set of real numbers less than 3.Therefore, graph the region on the number line to the left of 3. Use the symbol ) to denote that the endpoint, 3, is not included in the solution. Skill Practice Graph the solution sets. 1. 2. 3. 5 4 (( 0 TIP: Some textbooks use a closed circle or an open circle (● or ) rather than 73 A statement that involves more than one inequality is called a compound inequality. One type of compound inequality is used to indicate that one number is between two others. For example, the inequality means that In words, this is easiest to understand if we read the variable first: x is greater than and x is less than 5. The numbers satisfied by these two conditions are those between and 5. Graphing a Compound Inequality Graph the solution set of the inequality: Solution: means that 4.1 6 y 1.7 and 4 3 2 4.1 Shade the region of the number line greater than 4.1 and less than or equal to 1.7. Skill Practice Graph the solution set. 4. 0 y 8.5 4.1 6 y y 1.7 4.1 6 y 1.7 Example 2 2 2 2 6 x and x 6 5. 2 6 x 6 5 x 5 a y 6 0 ( 6 5 4 3 2 1 0 1 2 3 4 5 6 y 6 3 Answers 1. 2. 3. 4. 0 8.5 5 54 a bracket or parenthesis to denote inclusion or exclusion of a value on the real number line. For example, the solution sets for the inequalities are graphed here. 6 5 4 3 2 1 0 1 2 3 4 5 6 c 73 6 5 4 3 2 1 0 1 2 3 4 5 6 x 7 1 x 7 1 and c 73 ( 1 0 1 2 3 4 5 6 1.7 6 5
miller_beginning_intermediate_algebra_4e_ch1_3
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