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Name ________________________________________ Date __________________ Class__________________ LESSON 5-3 Practice A Solving Compound Inequalities Graph each inequality, and then graph the compound inequality. 1. x ! 3 2. z 0 xd4 z!2 intersection: x ! 3 AND x d 4 union: z 0 OR z ! 2 Write the compound inequality shown by each graph. 3. 4. _________________________________________ ________________________________________ Fill in the blanks to solve each compound inequality. Graph the solutions. 5. n 5 2 OR _____ _____ n _____ OR n5t9 6. 11 d 2x 1 d 1 _____ _____ 11 d 2x 1 n t _____ AND _____ _____ _____ d 2x _____ AND y _____ y _____ _____ dx 2x 1 d 1 2x d _____ y _____ AND _____ y _____ x d _____ Write a compound inequality for each problem. Graph the solutions. 7. To relieve arthritis, Dr. Stoll recommends taking between 400 and 600 mg of ibuprofen, inclusive. _____________________________________ 8. An advertisement for a part-time job says that the hourly rate is between $6.40 and $9.80 inclusive, depending on experience. _____________________________________ © Houghton Mifflin Harcourt Publishing Company 113 Holt McDougal Coordinate Algebra 4. all real numbers 6. x3 3x 11 5. n ! 12 y1 6. no solutions 5 7. x d 5 7 x y x y 4 7 4 1 2 5 3 2 0 3 2 5 2 1 1 8 4 1 0 11 8. z 0 9. no solutions 10. b ! 11 11. k ! 1 1 3 y2 12. d 610 13. decreased 2000 people each year 14. 350,000 2000y 15. increased 3000 people each year 16. 200,000 3000y 17. 350,000 2000y 200,000 3000y y ! 30 for years after 2010 Review for Mastery 1. add 6y to both sides x d 2 2. add 3p to both sides 3. add 3r to both sides Problem Solving 4. c ! 4 5. x 1. 5r ! 50 2r ; r ! 16 3 2 2. 25,000 1000y ! 19,000 1500y; y 12 3. 75m ! 510 60m; m ! 34 6. a ! 15 4. 15 5s ! 8s ; s 5 7. no solutions 5. B 8. all real numbers 6. F Reading Strategies 9. all real numbers 10. all real numbers 1. Left; so he divides by a positive number. 11. no solutions 2. t ! 8 Challenge 3. n ! 7; left; you do not have to switch the inequality symbol. 1. x 4; the lines intersect 2. x 4; the line for y1 is above (greater than) the line for y2 5-3 SOLVING COMPOUND INEQUALITIES 3. x 3 ! 2x 1 Practice A 4. x 4; same solutions as problem 2 1. 5. Possible answer: Find the x-values for which the line for y2 is either above (greater than) or intersects (equal to) the line for y1. The solutions are x t 4. © Houghton Mifflin Harcourt Publishing Company A17 Holt McDougal Coordinate Algebra 12. 140 w d 147 2. Practice C 1. 0.5 x 2 3. x d 1 OR x t 5 4. x ! 4 AND x d 1 2. a d 1 OR a t 6 5. 5; 5; 5; 5; 3; 4 3. y ! 8 OR y d 3; all real numbers 6. 1; 1; 1; 1; 10; 2; 2; 2; 2; 2; 5; 1 4. 4 d x d 1 7. 400 d m d 600 5. k ! 3 8. 6.40 d r d 9.80 6. z 14 OR z t 1.8 Practice B 1. 2 x 4 2. x 3 OR x t 3 3. x d15 OR x t 8 4. 0 d x 20 7. 8 d n d 10 5. 7 x 4 8. p ! 2 AND p d 6; no solutions 6. 3 d n 7 9. 0 A 4.55 OR A ! 8.75 7. 3 d b d 2 Review for Mastery 8. x 0 OR x t 6 1. 3 x 4 x 4 d 10 2. 8 d m 4 m 4 d 15 3. 9. k d 4 OR k t 4 10. s d 2 OR s ! 7 11. 20 d h d 20,000 4. 4 k 1 © Houghton Mifflin Harcourt Publishing Company A18 Holt McDougal Coordinate Algebra