additional exercises 4.1 i - breakthroughs happen herehpayne/math 152/additional...

Name __________________________________ Date _________________________

AE-117

Additional Exercises 4.1 Form I

Solving Linear Inequalities

Express each interval in set-builder notation and graph the interval on a number line. 1. (2, 5) 1. _______________ 2. (–1, 3] 2. _______________ 3. [–3, 3] 3. _______________ 4. [0, 4) 4. _______________ Solve each linear inequality. Other then Ø, graph the solution set on a number line. 5. 1192 !+x 5. _______________ 6. 1154 "#+x 6. _______________ 7. 53 "" x >4 7. _______________ 8. 1572 <+" x 8. _______________ 9. 10325 +#+ xx 9. _______________

Name __________________________________ Date _________________________

AE-118

10. 347 ""<" xx 10. ________________ 11. )2(48 +! xx 11. _______________ 12. )5(4)5(6 ">" xx 12. _______________ 13. When making a long distance call from a certain pay phone, 13. _______________ the first three minutes of a call cost $3.00. After that, each additional minute or portion of a minute cost $0.20. Use an inequality to find maximum number of minutes one can call long distance for $5.80. 14. It takes 20 minutes to set up a candy making machine. Once 14. _______________ the machine is set up, it produces 25 candies per minute. Use an inequality to find the number of candies that can be produced in 2 hours if the machine has not yet been set up. 15. A certain store has a fax machine available for use by its 15. _______________ customers. The store charges $1.75 to send the first page and $0.50 for each subsequent page. Use an inequality to find the maximum number of pages that can be faxed for $5.25.

Name __________________________________ Date _________________________

AE-123

Additional Exercises 4.2 Form I

Compound Inequalities

In exercises 1–7 , use the following sets to find the union or intersection. A = {1, 3, 5, 7, 9, 11} B = {1, 2, 3, 4, 5, 6} C = {2, 4, 6, 8} D = Ø 1. A ! B 1. _______________ 2. B " C 2. _______________ 3. C ! D 3. _______________ 4. A " C 4. _______________ 5. B " D 5. _______________ 6. A " B 6. _______________ 7. B ! C 7. _______________ (a) Solve the inequalities and write in set builder notation the (b) express the answer in interval notation. 8. 2>x and 4>x 8a. _______________ b. ______________ 9. 1>x or 3>x 9a. ______________ b. ______________ 10. 5#x and 2#x 10a. ______________ b. _____________

Name __________________________________ Date _________________________

AE-124

11. 3<x or 4–$x 11a. ______________ b. _____________ 12. 3<x and 0$x 12a. ______________ b. ______________ 13. 4$x or 2–<x 13a. ______________ b. ______________ 14. 5>x and 3–<x 14a. ______________ b. ______________ 15. 1028 <+< x 15a. ______________ b. ______________ 16. 16–4 <x and 21–3 >x 16a. ______________ b. ______________ 17. 4–2 <x or 102 >x 17a. ______________ b. ______________

Name __________________________________ Date _________________________

AE-125

Solve. Use interval notation to express the range. 18. The formula for converting Celsius temperature, 18. ______________ C, to Fahrenheit temperature, F, is 328.1 += CF . If Celsius temperature ranges from 45° to 115°, inclusive, what is the range for the Fahrenheit temperature? Round to the nearest whole number if necessary. 19. On the first four exams, your grades are 75, 87, 62, 19. _______________ and 76. There is still a final exam , and it counts as two grades. You are hoping to earn a C in the course. This will occur if the average of the six exam grades is greater than or equal to 70 and less then 80. What range of grades on the final will result in earning a C? 20. Parts for an automobile repair cost $468. The mechanic 20. _______________ charges $26 per hour. If you receive an estimate for at least $546 and the most $624 for fixing the car, what is the time interval that the mechanic will be working on the job?

Name __________________________________ Date _________________________

AE-132

Additional Exercises 4.3 Form I

Equations and Inequalities Involving Absolute Value

Find the solution set for each equation. 1. x = 5 1. _______________

2. 3!x = 8 2. _______________

3. 2+x = 4 3. _______________

4. 13 !x = 5 4. _______________

5. x = –7 5. _______________

6. 4+x = 0 6. _______________

7. 6!x = 0 7. _______________

8. 3 2+x = 9 8. _______________

9. 2 53 +x = 10 9. _______________

(a) Solve the inequality and then (b) graph the solution set. 10. 2>x 10. ______________

11. 3"x 11. _______________

Name __________________________________ Date _________________________

AE-133

12. 32 <!x 12. _______________

13. |x – 4| > 0 13. _______________ 14. |x – 6| ! 2 14. _______________ 15. |3x – 4| < 1 15. _______________ 16. |2x – 4| ! 2 16. _______________ 17. |2x + 5| " 3 17. _______________ 18. |5x + 2| > 7 18. _______________ The following table gives the percent of the viewing public that watched five television programs last week. Use the information in the table to answer exercises 19-20.

19. Express the percentage of the viewing public, x, that watched 19. _______________ Inside and Out last week as an absolute value inequality. The margin of error is ±2.4%. 20. Express the percentage of the viewing public, x, that watched 20. _______________ Guess Who? last week as a compound inequality. The margin of error is ±3.6%.

Program Viewing Percentage The Winstons 38.30% Guess Who? 42.50% Four to Go 27.90%

Inside and Out 16.40% Union Street 11.80%

Name __________________________________ Date _________________________

AE-138

Additional Exercises 4.4 Form I

Linear Inequalities in Two Variables

Graph the inequality. 1. 5!<+ yx 2. 4!" xy 3. xy #! 3 4. 2"y

Name __________________________________ Date _________________________

AE-139

Graph the solution set of the system of inequalities. 5. 2+> xy 3!!< xy 6. 3>+ yx 2!<+ yx 7. 42 <+ yx 12 !>+ yx 8. 422 !>+ yx 824 <+! yx 9. 1052 "+ yx 632 <! yx

Name __________________________________ Date _________________________

AE-140

10. 042 #! yx 844 !"+ yx 11. 43 <#! x 12. 2#x 2!<y 13. 1!"x 3+# xy 4+!" xy 14. 2#y 42 +# xy 13 +!" xy

Name __________________________________ Date _________________________

AE-137

12. 972 "++x 12. _______________

13. 24|78| !<+!x 13. _______________ 14. 15|55| <!!x 14. _______________

15. 24|78| !<+!x 15. _______________ 16. 3|4x – 1| + 3 > 12 16. _______________ 17. –4|1 – x| < –8 17. _______________ 18. –2|4 –x| ! –10 18. _______________ The following table gives the percent of the viewing public that watched five television programs last week. Use the information in the table to answer exercises 19-20.

19. Express the percentage of the viewing public, x, that watched 19. _______________ Inside and Out last week as an absolute value inequality. The margin of error is ±3.1%. 20. Express the percentage of the viewing public, x, that watched 20. _______________ The Winstons last week as a compound inequality. The margin of error is ±1.5%.

Program Viewing Percentage The Winstons 38.30% Guess Who? 42.50% Four to Go 27.90%

Inside and Out 16.40% Union Street 11.80%