Section 3.5 Linear Inequalities and Systems of Linear Inequalities in Two Variables 277 Section 3.5 Practice Exercises Vocabulary and Key Concepts 1. a. An inequality that can be written in the form is called a inequality in two variables. Ax By 7 C b. Given the inequality the boundary line (is/is not) included in the solution set. 3x 4y 6 6, 3x 4y 6 However, given 3x 4y 6, then the boundary line (is/is not) included in the solution set. c. Given the inequality the boundary line should be drawn as a (solid/dashed) line 5x y 7 5, 5x y 5 to indicate that the line (is/is not) part of the solution set. d. Given the inequality y x 4, the boundary line y x 4 should be drawn as a (solid/dashed) line to indicate that the line (is/is not) part of the solution set. Review Exercises For Exercises 2–5, solve the inequalities. Write the solution set in interval notation. 5 6 x 1 and 2x 6 6 5 x 4 and 6 7 3x 3 2. 3. 4 y 6 3y 12 or 21y 32 2x 6 4 or 3x 1 13 12 4. 5. Concept 1: Graphing Linear Inequalities in Two Variables For Exercises 6–9, decide if the given point is a solution to the inequality. 6. 7. 2x y 7 8 3y x 6 5 1 15, 02 1 1, 72 13, 52 1, 102 a. b. a. b. c. d. 10, 02 c. 10, 02 d. 14, 22 12, 32 8. 9. a. b. a. 14, 52 b. c. 10, 02 d. 13, 22 c. (8, 8) d. (0, 0) 1 15, 12 15, 32 4, 22 10. When should you use a dashed line to graph the solution to a linear inequality? For Exercises 11–16, decide which inequality symbol should be used by looking at the graph. 11. 12. 13. y 5 3 2 1 21 1 5 y 3 2 1 21 1 x y 2 y 2x 3 y 4 y x 1 2 3 4 5 5 4 3 2 1 1 1 2 3 5 5432 4 543 1 2 3 4 5 2 3 4 5 x 4 543 1 2 3 4 5 2 3 4 5 x 16, 7, , 2 y 2 x 5
miller_intermediate_algebra_4e_ch1_3
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