Equations & Inequalities Chapter Questions

Equations & Inequalities Chapter Questions 1. When given a set of possible solutions to an equation or inequality, how do you determine which are solutions? 2. What are inverse operations? Name them. 3. How do you solve equations? 4. How do we translate a statement into an inequality? 5. Explain the steps to graphing an inequality on a number line. NJ Center for Teaching and Learning ~ 1 ~ www.njctl.org

Solving Equations Chapter Problems Writing Equations Classwork 1. Larry has 14 toy cars. His grandparents give him some more toy cars. Now he has 22 toy cars. Write an equation that can be used to determine how many toy cars Larry s grandparent s give him. 2. Kenya did 16 pull-ups at the end of the month. This was 4 times as many pull-ups as she was able to do at the beginning of the month. Write an equation that can be used to find the number of pull-ups Kenya could do at the beginning of the month. 3. Tracy worked 28 hours this week. That was 3 hours less than Frank worked. Write an equation to figure out how many hours Frank worked. 4. During the school Walk-a-Thon, each class completed an average of 64 laps around the track. The school completed 832 laps all together. Write an equation to represent the number of classes that participated in the Walk-a-Thon. Homework 5. Jennifer bought 3 bags of trail mix to make snack packs. She made 18 snacks packs with the trail mix. Write an equation to represent the number of snack packs each bag of trail mix made. 6. Samantha, who is 3 years older than Francis, is 12. Write an equation to represent Francis age. 7. Frederick is half as tall as his older sister. His older sister is 62 inches tall. Write an equation to represent Frederick s height. 8. Franco bought a bag of 25 jolly ranchers. After sharing with his friends, he had 13 left. Write an equation to represent the number of jolly ranchers he shared with his friends. Determining Solutions to Equations Classwork 9. Use the solution set to determine the solution to each equation. a. x + 12 = 20 {5, 6, 7, 8} b. x - 13 = 32 {43, 44, 45, 46} c. 2x + 4 = 26 {9, 10, 11, 12} d. 5y 3 = 57 {9, 10, 11, 12} e. 4x + 3 = 15 {3, 4, 5, 6} f. 5p 4 = 16 {3, 4, 5, 6} g. 5g + 15 = 25 {1, 2, 3, 4} h. 7h 14 = 42 {8, 9, 10, 11} Homework 10. Use the solution set to determine the solution to each equation. a. x + 19 = 33 {12, 13, 14, 15} b. x - 12 = 26 {35, 36, 37, 38} c. 4x + 9 = 45 {7, 8, 9, 10} d. 5y - 19 = 16 {5, 6, 7, 8} e. 7g + 17 = 45 {4, 5, 6, 7} f. 9h - 4 = 41 {3, 4, 5, 6} g. 6m + 13 = 79 {8, 9, 10, 11} h. 8x 7 = 57 {5, 6, 7, 8} NJ Center for Teaching and Learning ~ 2 ~ www.njctl.org

Inverse Operations Classwork 11. Name the inverse operation needed to solve for the variable. a. x + 9 = 17 b. y 8 = 5 c. m + 5 = 21 w d. 6 12 e. 9v = 108 Homework 12. Name the inverse operation needed to solve for the variable. a. t 18 = 54 b. 14x = 228 c. m + 19 = 51 d. 11b = 66 m e. 4 2 13. When solving an equation, why do you apply the inverse of the given operation to both sides? Solving One Step Equations with Addition and Subtraction Classwork 14. Solve. a. n + 7 = 20 b. x + 9 = 28 c. a + 15 = 27 d. y + 29 = 35 e. 50 + w = 92 f. 4 + m = 18 g. x 6 = 15 h. y 19 = 27 i. m 56 = 32 j. x 9 = 72 k. y 17 = 56 l. z 5 = 98 Homework 15. Solve. a. n + 9 = 13 b. 14 + b = 21 c. z + 18 = 42 d. 7 + g = 63 e. 19 = 15 + y f. b + 4 = 71 g. x 7 = 16 h. y 25 = 34 i. m 19 = 39 NJ Center for Teaching and Learning ~ 3 ~ www.njctl.org

j. y 13 = 67 k. z 43 = 57 l. x 32 = 77 Solving One Step Equations with Multiplication and Division Classwork 16. Solve. a. 7x = 84 b. 30 = 12m c. 5m = 25 d. 10c = 80 e. 13m = 143 f. 9y = 126 g. h. i. j. k. l. x 5 = 13 y 4 = 12 z 8 = 10 x 7 = 25 x = 45 9 y = 62 5 Homework 17. Solve. a. 18x = 360 b. 17y = 51 c. 9p = 99 d. 15c = 75 e. 8r = 136 f. 6x = 108 g. h. i. j. k. l. x 5 = 12 y 4 = 13 z 8 = 40 x 7 = 35 x = 56 9 y = 26 5 Writing Simple Inequalities Classwork 18. Write an inequality for each sentence below. a. y is less than 8. b. f is greater than -5. c. j is greater than or equal to 4. d. The speed limit, s, cannot exceed 55 mph. e. 10 is less than or equal to x. NJ Center for Teaching and Learning ~ 4 ~ www.njctl.org

Homework f. A number, x is at least 15. g. A number, h is not greater than 4. h. x is not more than 20. i. A number, z, is negative. j. To have a passing grade, g, must exceed a 70. k. k is less than or equal to -3. l. The total, t, is fewer than 8 items. m. -2 is less than a number, n. n. The time, t, on your quiz cannot exceed 20 minutes. o. At most, 4 students, s, will fail the test. 19. Write an inequality for each sentence below. a. w is greater than 7. b. p is less than or equal to -1. c. m is less than 5. d. 11 is greater than or equal to k. e. A number, f is positive. f. The total, t is fewer than 4 items. g. 4 is less than a number, n. h. The speed limit, s, cannot exceed 25 mph. i. A number c is at least 12. j. w is not more than 50. k. g is more than or equal to 8. l. h is not less than -5. m. The time, t for lunch cannot exceed 30 minutes. n. At most, 25 students, s, will be in the class. o. To have an A in class, g, must exceed a 92. Solutions to Simple Inequalities Classwork 20. Use the solution set to determine the solutions to each inequality. a. x < 17 {15, 16, 17, 18} b. m > 9 {8, 9, 10, 11} c. r < 9 {7, 8, 9, 10} d. b > 23 {21, 22, 23, 24} e. m < 27 {26, 27, 28, 29} f. 3r > 18 {4, 5, 6, 7} g. 8y < 24 {2, 3, 4, 5} h. 9x < 45 {4, 5, 6, 7} Homework 21. Use the solution set to determine the solutions to each inequality. a. y > 14 {13, 14, 15, 16} b. x < 16 {14, 15, 16, 17} c. m < 9 {8, 9, 10, 11} d. g > 13 {12, 13, 14, 15} e. x < 32 {31, 32, 33, 34} NJ Center for Teaching and Learning ~ 5 ~ www.njctl.org

f. 4y > 32 {6, 7, 8, 9} g. 3g > 26 {12, 13, 14, 15} h. 7m < 56 {6, 7, 8, 9} Graphing Solution Sets to Simple Inequalities Classwork 22. Write an inequality for the graph below. 23. Write an inequality for the graph below. 24. Write an inequality for the graph below. 25. Write an inequality for the graph below. NJ Center for Teaching and Learning ~ 6 ~ www.njctl.org

26. Write an inequality for the graph below. 27. Write an inequality for the graph below. 28. Graph the solution for each inequality. a. w > 7 b. p < -1 c. m < 5 d. 11 k e. f > 0 f. t < 4 g. 4 < n 29. Write an inequality for each sentence below, and then graph the solutions of each inequality on a number line. a. x is less than fifteen. b. y cannot exceed twenty. c. Twenty is less than or equal to m. d. The cost, c, is more than $50. e. Twelve is greater than or equal to b. Homework 30. Write an inequality for the graph below. 31. Write an inequality for the graph below. NJ Center for Teaching and Learning ~ 7 ~ www.njctl.org

32. Write an inequality for the graph below. 33. Write an inequality for the graph below. 34. Write an inequality for the graph below. 35. Write an inequality for the graph below. 36. Graph the solution for each inequality a. s < 25 b. x 12 c. w < 50 d. g 8 e. h -5 f. t < 30 g. 25 s 37. Write an inequality for each sentence below, and then graph the solutions of each inequality on a number line. a. y is greater than nine. b. x is less than or equal to sixteen. c. Nineteen is greater than m. d. Your height, h, must exceed 42 inches. e. The weight limit, w, is 225 pounds. NJ Center for Teaching and Learning ~ 8 ~ www.njctl.org

Equations and Inequalities Multiple Choice Problems 1. Use the solution set to determine the solution to 4x = 68 {16, 17, 18, 19} a. 16 b. 17 c. 18 d. 19 2. Use the solution set to determine the solution to 3x 5 = 22 {7, 8, 9, 10} a. 7 b. 8 c. 9 d. 10 3. Name the inverse operation used to solve this equation: x 7 = 13 a. Multiplication b. Division c. Addition d. Subtraction 4. Name the inverse operation used to solve this equation: x 3 = 21 a. Multiplication b. Division c. Addition d. Subtraction 5. Name the inverse operation used to solve this equation: 5x = 25 a. Multiplication b. Division c. Addition d. Subtraction 6. Name the inverse operation used to solve this equation: x + 9 = 27 a. Multiplication b. Division c. Addition d. Subtraction 7. Solve the equation: 12x = 96 a. x = 1152 b. x = 8 c. x = 9 d. x = 84 8. Solve the equation: y + 36 = 43 a. y = 7 b. y = 79 c. y = 8 d. y = 78 NJ Center for Teaching and Learning ~ 9 ~ www.njctl.org

9. Solve the equation: p 12 = 56 a. p = 44 b. p = 4 c. p = 5 d. p = 68 10. Solve the equation: x 5 = 12 a. x = 7 b. x = 2 c. x = 60 d. x = 3 11. Translate into an inequality: A number, x, is less than 35. a. x < 35 b. x > 35 c. x > 35 d. x < 35 12. Translate into an inequality: the speed, s, cannot exceed 55 mph. a. s < 55 b. s > 55 c. s > 55 d. s < 55 13. Translate into an inequality: the people in attendance at the concert, p, exceeds 1,200. a. p < 1,200 b. p > 1,200 c. p > 1,200 d. p < 1,200 14. Translate into an inequality: the number 13, is less than or equal to the number of spots, s, on the dog. a. s < 13 b. s > 13 c. s > 13 d. s < 13 Equations and Inequalities Short Constructed Response Questions 1. Use the solution set to determine the solutions to: p < 12 {10,11,12,13} 2. Use the solution set to determine the solutions to: 11r > 36 {2, 3, 4, 5} 3. Use the solution set to determine the solutions to: x 32 < 4 {34, 35, 36, 37} NJ Center for Teaching and Learning ~ 10 ~ www.njctl.org

4. Use the solution set to determine the solutions to: y + 25 > 39 {12, 13, 14, 15} 5. James, who is 14, is three times younger than his father. Write and solve an equation to determine his father s age. 6. A shipping company packs crates of milk. They packed 23 crates with 32 milk jugs each. Write and solve an equation to find the total number of milk jugs they packed. 7. Marcus has 19 his rare coin collection. His brother also collects rare coins. Together, they have 43 rare coins. Write and solve an equation to show how many coins are in his brother s collection. 8. Write the inequality for the graph below. 9. Write the inequality for the graph below. 10. Write the inequality for the graph below. 11. Write the inequality for the graph below. NJ Center for Teaching and Learning ~ 11 ~ www.njctl.org

Equations and Inequalities Extended Constructed Response 1. Fourteen less than the amount of money, m, is less than or equal to $35. a. Model with an inequality. b. Use the solution set to determine the solution to the inequality. {49, 50, 51, 52} c. Graph the solution to the inequality. 2. Three times the weight, w, is greater than 336 pounds. a. Model with an inequality. b. Use the solution set to determine the solution to the inequality. {110, 111, 112, 113} c. Graph the solution to the inequality. 3. Thirty-three more than a number, x, is 57. a. Model with an equation. b. Solve the equation for x. c. Explain how you found the solution to the equation. NJ Center for Teaching and Learning ~ 12 ~ www.njctl.org

4. Maria runs 7 miles every week. At the end of n weeks, she ran 91 miles. a. Model with an equation. b. Solve the equation for n. c. Write and solve an equation to determine the number of miles she would run in a year if she continued running at this rate. NJ Center for Teaching and Learning ~ 13 ~ www.njctl.org

CW-HW Answer Key 1. 14 + x = 22 2. 4x = 16 3. x-3 = 28 4. 832/x=64 5. 18/3 = x 6. x + 3 = 12 7. 62/2 = x 8. 25 - x = 13 9. a. 8 b. 45 c. 11 d. 12 e. 3 f. 4 g. 2 h. 8 10. a. 14 b. 38 c. 9 d. 7 e. 4 f. 5 g. 11 h. 8 11. a. Subtraction b. Addition c. Subtraction d. Multiplication e. Division 12. a. Addition b. Division c. Subtraction d. Division e. Multiplication 13. The equals sign indicates that both sides of the equation are equal. If we change one side of the equation, but not the other, then the two sides will no longer be equal. 14. a. 13 b. 19 c. 12 d. 6 e. 42 f. 14 g. 21 h. 46 i. 88 j. 81 k. 73 l. 103 15. a. 4 b. 7 c. 24 d. 56 e. 4 f. 67 g. 23 h. 59 i. 58 j. 80 k. 100 l. 109 16. a. 12 b. 2.5 c. 5 d. 8 e. 11 f. 14 g. 65 h. 48 i. 80 j. 175 k. 405 l. 310 17. a. 20 b. 3 c. 11 d. 5 e. 17 f. 18 g. 60 h. 52 i. 320 j. 245 k. 504 l. 130 18. a. y < 8 b. f > -5 c. j 4 d. s < 55 e. 10 < x f. x > 15 g. h < 4 h. x < 20 i. z < 0 j. g > 70 k. k < -3 l. t < 8 m. -2 < n n. t < 20 o. s < 4 NJ Center for Teaching and Learning ~ 14 ~ www.njctl.org

19. a. w > 7 b. p < -1 c. m < 5 d. 11 k e. f > 0 f. t < 4 g. 4 < n h. s < 25 i. c 12 j. w < 50 k. g 8 l. h -5 m. t < 30 n. s < 25 o. g > 92 20. a. {15,16} b. {10,11} c. {7,8} 28. a. d. {23,24} e. {26,27} f. {7} g. {2,3} h. {4} 21. a. {14,15,16} b. {14,15} c. {8,9} d. {13,14,15} e. {31} f. {8,9} g. {12,13,14,15} h. {6,7,8} 22. x > -2 23. x < 7 24. x 2 25. x < 6 26. x < 5 27. x -75 b. c. d. e. f. g. 29. a. x < 15 b. y < 20 c. 20 < m d. c > 50 NJ Center for Teaching and Learning ~ 15 ~ www.njctl.org

e. 12 > b 30. x -6 31. x < -2 32. x < 4 33. x > 0 34. x > -10 35. x 2.5 36. a. b. c. d. e. f. g. 37. a. y > 9 b. x < 16 c. 19 > m d. h > 42 e. w < 225 NJ Center for Teaching and Learning ~ 16 ~ www.njctl.org

Equations and Inequalities Multiple Choice Problems 1. b 2. c 3. c 4. a 5. b 6. d 7. b 8. b 9. d 10. c 11. d 12. a 13. b 14. c Equations and Inequalities Short Constructed Response Questions 1. 10, 11, 12 2. 4, 5 3. 34, 35, 36 4. 15 5. 14=x/3 6. 23(32)=x 7. 19+x=43 8. x > -6 9. x < 2 10. x < - 1 4 11. x > 5 Equations and Inequalities Extended Constructed Response Questions 1. a. m 14 < 35 b. 49 c. 2. a. 3w > 336 b. 113 c. 3. 4. a. x + 33 = 57 b. x + 33 = 57-33 -33 x = 24 c. I used the inverse operation of addition, which is subtraction, to solve this equation. I subtracted 33 from both sides of the equation to get 24 for the value of x. a. 7n = 91 b. 7n = 91 7 7 n = 13 Maria ran for 13 weeks. c. 52(7) = x 364 = x If Maria continues at this rate, she will run 364 miles in a year. NJ Center for Teaching and Learning ~ 17 ~ www.njctl.org

NJ Center for Teaching and Learning ~ 18 ~ www.njctl.org