Writing Inequalities

1. Writing Inequalities

2. Translate the following sentences into inequalities. 1) A number is greater than 16.2) A number is less than 16.3) A number is at least 16. 4) A number is at most 16.

3. Translate the following sentences into inequalities. 1) A number is greater than 16. N > 162) A number is less than 16.3) A number is at least 16. 4) A number is at most 16.

4. Translate the following sentences into inequalities. 1) A number is greater than 16. N > 162) A number is less than 16. N < 163) A number is at least 16. 4) A number is at most 16.

5. Translate the following sentences into inequalities. 1) A number is greater than 16. N > 162) A number is less than 16. N < 163) A number is at least 16. N ≥ 164) A number is at most 16.

6. Translate the following sentences into inequalities. 1) A number is greater than 16. N > 162) A number is less than 16. N < 163) A number is at least 16. N ≥ 164) A number is at most 16. N ≤ 16

7. Translate the following phrases into mathematical expressions. 1) Three times a number decreased by four.2) Five more than twice a number.3) The sum of two consecutive integers.4) The sum of two consecutive even integers.

8. Translate the following phrases into mathematical expressions. 1) Three times a number decreased by four.3N - 42) Five more than twice a number.3) The sum of two consecutive integers.4) The sum of two consecutive even integers.

9. Translate the following phrases into mathematical expressions. 1) Three times a number decreased by four.3N - 42) Five more than twice a number.5 + 2N3) The sum of two consecutive integers.4) The sum of two consecutive even integers.

10. Translate the following phrases into mathematical expressions. 1) Three times a number decreased by four.3N - 42) Five more than twice a number.5 + 2N3) The sum of two consecutive integers.N + N + 14) The sum of two consecutive even integers.

11. Translate the following phrases into mathematical expressions. 1) Three times a number decreased by four.3N - 42) Five more than twice a number.5 + 2N3) The sum of two consecutive integers.N + N + 14) The sum of two consecutive even integers.N + N + 2

12. For each of the following problems: 1) Define a variable.2) Write an inequality.3) Solve the inequality.

13. 1) Three times a number increased by 8 is at least 25. What is the number?

14. 1) Three times a number increased by 8 is at least 25. What is the number? N = the number

15. 1) Three times a number increased by 8 is at least 25. What is the number? x 3 + 8 ≥ N = the number 3N + 8 ≥ 25

16. 1) Three times a number increased by 8 is at least 25. What is the number? x 3 + 8 ≥ N = the number 3N + 8 ≥ 25N ≥ 5 2/3

17. 2. The sum of 20 and x is greater than 30. What is the number?

18. 3) The quotient of x and 20 is greater than or equal to 30. What is the number?

19. 4) The difference of 4 and x is at most 30. What is the number?

20. 5) Women’s Sports & Fitness Magazine states that three times the weight of a backpack and its contents should be less than your body weight to avoid injury. How much weight can you put in your backpack if your empty pack weighs 15 pounds and if your weight is 120 pounds?

21. 2) Women’s Sports & Fitness Magazine states that three times the weight of a backpack and its contents should be less than your body weight to avoid injury. How much weight can you put in your backpack if your empty pack weighs 15 pounds and if your weight is 120 pounds? W = weight of contents

22. 2) Women’s Sports & Fitness Magazine states that three times the weight of a backpack and its contents should be less than your body weight to avoid injury. How much weight can you put in your backpack if your empty pack weighs 15 pounds and if your weight is 120 pounds? + x 3 ( < ) W = weight of contents 3(W + 15) < 120

23. 2) Women’s Sports & Fitness Magazine states that three times the weight of a backpack and its contents should be less than your body weight to avoid injury. How much weight can you put in your backpack if your empty pack weighs 15 pounds and if your weight is 120 pounds? + x 3 ( < ) W = weight of contents 3(W + 15) < 120W < 25

24. 6) The sum of two consecutive odd integers is more than 136. Find the least pair of such integers.

25. 3) The sum of two consecutive odd integers is more than 136. Find the least pair of such integers. i = the first odd integeri + 2 = the second odd integer

26. + 3) The sum of two consecutive odd integers is more than 136. Find the least pair of such integers. > i = the first odd integeri + 2 = the second odd integeri + i + 2 > 136

27. + 3) The sum of two consecutive odd integers is more than 136. Find the least pair of such integers. > i = the first odd integeri + 2 = the second odd integeri + i + 2 > 136i > 67Therefore, the integers must be 69 and 71.

28. 4) The sum of two consecutive integers is at least 35. Find the integers.

29. 4) The sum of two consecutive integers is at least 35. Find the integers. i = the first integeri + 1 = the next integer

30. 4) The sum of two consecutive integers is at least 35. Find the integers. + ≥ i = the first integeri + 1 = the next integeri + i + 1 ≥ 35

31. 4) The sum of two consecutive integers is at least 35. Find the integers. + ≥ i = the first integeri + 1 = the next integeri + i + 1 ≥ 35i ≥ 17Therefore, the integers are 17 and 18.