Chap4 Section4

Elementary and Intermediate Algebra: Graphs & Models (3rd Edition)

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Section 4.4 Absolute Value Inequalities 405 Version: Fall 2007 4.4 Exercises For each of the inequalities in Exercises 1 - 10 , perform each of the following tasks. i. Set up a coordinate system on a sheet of graph paper. Label and scale each axis. ii. Sketch the graph of each side of the inequality without the aid of a cal- culator. Label each graph with its equation. iii. Shade the solution of the inequality on the x -axis (if any) in the manner shown in Figures 4 and 8 in the narra- tive. That is, drop dashed lines from the points of intersection to the axis, then shade and label the solution set on the x -axis. Use set-builder and interval notation (when possible) to describe your solution set. 1. | x | > 2 2. | x | > 0 3. | x | < 3 4. | x | > 2 5. | x | > 1 6. | x | < 4 7. | x | ≤ 0 8. | x | ≤ − 2 9. | x | ≤ 2 10. | x | ≥ 1 Copyrighted material. See: 1 For each of the inequalities in Exercises 11 - 22 , perform each of the following tasks. i. Load each side of the inequality into the Y= menu of your calculator. Ad- just the viewing window so that all points of intersection of the two graphs are visible in the viewing window. ii. Copy the image in your viewing screen onto your homework paper. Label each axis and scale each axis with xmin, xmax, ymin, and ymax. La- bel each graph with its equation. iii. Use the intersect utility in the CALC menu to determine the points of in- tersection. Shade the solution of the inequality on the x -axis (if any) in the manner shown in Figures 4 and 8 in the narrative. That is, drop dashed lines from the points of intersection to the axis, then shade and label the solution set on the x -axis. Use set- builder and interval notation (when appropriate) to describe your solution set. 11. | 3 2 x | > 5 12. | 2 x + 7 | < 4 13. | 4 x + 5 | < 7 14. | 5 x 7 | > 8 15. | 4 x + 5 | > 2 16. | 3 x 5 | < 3 17. | 2 x 9 | ≥ 6 18. | 3 x + 25 | ≥ 8
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406 Chapter 4 Absolute Value Functions Version: Fall 2007 19. | 13 2 x | ≤ 7 20. | 2 x + 15 | ≤ 7 21. | 3 x 11 | > 0 22. | 4 x + 19 | ≤ 0 For each of the inequalities in Exercises 23 - 32 , provide a purely algebraic solution without the use of a calculator. Show all of your work that leads to the solu- tion, shade your solution set on a num- ber line, then use set-builder and interval notation (if possible) to describe your so- lution set. 23. | 4 x + 3 | < 8 24. | 3 x 5 | > 11 25. | 2 x 3 | ≤ 10 26. | 3 5 x | ≥ 15 27. | 3 x 4 | < 7 28. | 5 2 x | > 10 29. | 3 7 x | ≥ 5 30. | 2 11 x | ≤ 6 31. | x + 2 | ≥ − 3 32. | x + 5 | < 4 For each of the inequalities in Exercises 33 - 38 , perform each of the following tasks. i. Arrange each of the following parts on your homework paper in the same location. Do not do place the alge- braic work on one page and the graph- ical work on another. ii. Follow each of the directions given for Exercises 11 - 22 to find and record a solution with your graphing calcu- lator. iii. Provide a purely algebraic solution, showing all the steps of your work.
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