Activities

1. Is x = -4 a solution to the inequality  -4 < 2x + 4 < 5?

2. What are the solutions to the inequality -1 ≤ x + 3 ≤ 7?

3. What are the solutions to the inequality 3 < 2b + 5 ≤ 11?

4. What are the solutions to the inequality x – 3 > 4 or 4x + 1 < 17?

5. Graph the solutions to the inequality -3 < m ≤ 2 on the number line below.

6. Graph the solutions to the inequality 6 > k ≥ -9 on the number line below.

7. Solve and graph the following compound inequality 4 – m < -2 or 12 < -5m + 2 .

8. Solve and graph the following inequality |2m| ≥ 8.

9. What is one integer solution to this inequality |1 – 2x| < 2?

10. Solve and graph the solution set for the following |3m – 4| + 2 < 10.

11. Determine the integer values of a and b so that a ≤ x – 3 ≤ b would use the following graph to display its solutions.

12. A certain math teacher made the claim that all of his students test scores would be contained within the solution set of the absolute value inequality |2x – 165| < 30. Since all scores were integers, what were the highest and lowest scores on the test?

13. A certain type of trout is said to have an average length, l, of 12 inches when it is 4 years old. But due to various environmental factors it may have grown at a different rate. The absolute value inequality |l – 12| ≤ 4.5 shows the range of trout length after 4 years of life. What is the largest and smallest size trout after 4 years?

14. Circle M has a radius that is between 4 and 8 inches. Write a compound inequality that can be used to show the smallest and largest area of circle M.

15. Why does the “OR” inequality below have inequality signs that both point in the same direction?

5 + x > 10        OR      5 – x > 10

16. Determine the values for a and b so that |ax + b| ≥ 8 has solutions which match the graph shown here.

17. Write a compound inequality to combine the following inequalities.

- 27 < 3x + 9              5x + 15 < 75

18. A funny math teacher gave her students a homework assignment with 120 problems on it. She then gave her students the following compound inequality 5 + 3p > 62 or 7 – p > -120. Finally, she told the students that they could choose the first or second part of the compound inequality. But based on whichever part they chose, their solution for p determined how many problems from the worksheet they had to complete for homework. Which inequality should her students choose and why?

Answer Key/Rubric

1. No
2. -4 ≤ x ≤ 4
3. -1 < b ≤ 3
4. x > 7 or x < 4
5. 
   
6. 
   
7. m > 6 or m < -2

8. m ≥ 4 or m ≤ -4

9. 0 or 1
10. (-4/3) < m < 4

11. a = -6 and b = 1
12. highest score 97%, lowest score 68%
13. largest trout 16.5 inches, smallest trout 7.5 inches
14. 16π ≤ area ≤ 64π inches²   or   50.3 ≤ area ≤ 201.1 inches²
15. The inequality signs do not point in the same direction because when you solve the second inequality you need to multiply or divide by negative one, and when you do that, you must reverse the inequality sign.
16. a = 2 and b = 4
17. -9 < x + 3 < 15
18. The students should chose the 2^nd part of the compound inequality because the solution is p < 127. This means that the students could do any number of problems less than 127, including 0 problems.