Chap4 Section3

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

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Section 4.3 Absolute Value Equations 385 Version: Fall 2007 4.3 Exercises For each of the equations in Exercises 1 - 4 , 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 equation without the aid of a calcula- tor. Label each graph with its equa- tion. iii. Shade the solution of the equation on the x -axis (if any) as shown in Figure 5 (read "Expectations") in the narrative. That is, drop dashed lines from the points of intersection to the axis, then shade and label the solu- tion set on the x -axis. 1. | x | = 2 2. | x | = 0 3. | x | = 3 4. | x | = 2 For each of the equations in Exercises 5 - 8 , perform each of the following tasks. i. Load each side of the equation 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- Copyrighted material. See: 1 tersection. Shade and label each so- lution as shown in Figure 5 (read "Ex- pectations") 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. 5. | 3 2 x | = 5 6. | 2 x + 7 | = 4 7. | 4 x + 5 | = 7 8. | 5 x 7 | = 8 For each of the equations in Exercises 9 - 14 , provide a purely algebraic solution without the use of a calculator. Arrange your work as shown in Examples 6, 7, and 8 in the narrative, but do not use a calculator. 9. | 4 x + 3 | = 0 10. | 3 x 11 | = 5 11. | 2 x + 7 | = 14 12. | 7 4 x | = 8 13. | 3 2 x | = 1 14. | 4 x + 9 | = 0 For each of the equations in Exercises 15 - 20 , 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-
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386 Chapter 4 Absolute Value Functions Version: Fall 2007 braic work on one page and the graph- ical work on another. ii. Follow each of the directions given for Exercises 5 - 8 to find and record a solution with your graphing calcula- tor. iii. Provide a purely algebraic solution, showing all the steps of your work. Do these solutions compare favorably with those found using your graphing calculator in part (ii)? If not, look for a mistake in your work. 15. | x 8 | = 7 16. | 2 x 15 | = 5 17. | 2 x + 11 | = 6 18. | 5 x 21 | = 7 19. | x 12 | = 6 20. | x + 11 | = 5 Use a strictly algebraic technique to solve each of the equations in Exercises 21 - 28 . Do not use a calculator. 21. | x + 2 | − 3 = 4 22. 3 | x + 5 | = 6 23. 2 | 3 2 x | = 6 24. | 4 x | + 5 = 12 25. 3 | x + 2 | − 5 = | x + 2 | + 7 26. 4 3 | 4 x | = 2 | 4 x | − 1 27. x 3 1 4 = 1 12 28. x 4 1 2 = 2 3 Use the technique of distance on the num- ber line demonstrated in Examples 16 and 17 to solve each of the equations in Exercises 29 - 32 . Provide number line sketches on your homework paper as shown in Examples 16 and 17 in the narrative.
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