Activities

1. Is x = 4 a solution to the inequality below?

2. Graph the solutions to the inequality x ≥ 0 on the number line below.

3. Write the inequality that is shown in the graph below.

4. List ten non-integer values that are part of the solution set graphed here.

5. What is the greatest integer that is not a solution to (a) x > 3 and the greatest integer that is a solution to (b) x ≤ 3.

6. Solve and graph the inequality 3 > 5 – x below.

7. If the values of –x are graphed below, write an inequality for x.

8. If the values of 2x – 3 are shown in the graph below, graph the solution set for x.

9. Sandra needs to graph the solutions to –x > 3, explain in detail how Sandra should proceed.

10. Todd was asked to graph the solution set to -2x – 3 ≤ -1. Identify the two mistakes Todd made if his result looked like the graph shown here.

11. Solve and graph this inequality:  -3(x – 2) < -2x – 1 .

12.  Explain why the inequality sign is reversed when multiplying or dividing an inequality by a negative number.

13. Graph the values that make this statement true on the number line below: .

14. If negative two times a number decreased by three is less than or equal to negative three times the same number, then how can you describe all of the values that number could be?

15. Solve and graph the following inequality -6b < 7b.

16. Graph the solution set to the inequality 2x + 7 – x ≤ 4(x – 2) – 3x.

17. Three inequalities are graphed below. Determine three values that are solutions for all three inequalities.

18. Determine values for a, b, and c so that ax + b > c includes the solutions graphed below.

19. Solve and graph the following inequality:  .

20. How many fewer solutions does x > 0 have than x > 100?

21. The graph of x > a, has an open circle at ‘a’ on the number line below and is shaded to the right. In terms of a, describe where the open circle would be plotted for 2x, -x and x/2.

22. Create an interesting story, involving money, which would use the inequality graphed below to describe the solution to an inequality problem.

23.  An interesting square has measurements such that the area is one sixteenth of the perimeter. Graph the amount of these interesting squares (s) that could fit inside a two inch by four inch rectangle.

Answer Key/Rubric

1. No

3. x ≥ -2

4. Various answers including: 3.1, π, 22/7, 3.5, 4.5,

5. (a) 3, (b) 3

6. x > 2,

7. x > -2

9. First, Sandra needs to recognize that she must isolate the variable x. She can do this by multiplying or dividing by -1 on both sides of her inequality. When she does this, in order to continue to make the inequality true, she must reverse the inequality sign. Her result is x < -3. Next, Sandra needs to graph her solutions on the number line. She begins by using an open circle to indicate that the number -3 is not included in the solution. Finally, Sandra shades the number line to the left of -3, indicating that the solutions for the original inequality are all the numbers to the left of -3.

10. First, Todd did not recognize that the inequality sign includes “or equal to” meaning that at his starting point he should fill in the circle. Secondly, Todd probably forgot to reverse the inequality sign when he multiplied or divided by a negative number. His final answer should include a filled in circle at -1 with all of the answers shaded to the right of -1 on the number line.

12. Various answers including: When you multiply or divide a true inequality statement by a negative both numbers (regardless of their original sign) flip to the opposite side of zero on a number line. This makes the most sense when one original number is positive and the other negative. In this case, when multiplied (or divided) by a negative the positive number becomes negative and the negative is now positive. Since they are now on the opposite sides of zero the inequality sign needs to be reversed in order for the inequality to remain true. You can picture the other two scenarios, when both numbers were negative or positive to start with, and see that the sign must be reversed in those cases as well.

14. The number is less than or equal to 3

15. b > 0,

16. No solutions,

17. -2, -1.5, -1

18. Various answers including: a = 2, b = -2, c = -20

19. All real numbers,

20. None, they both have an infinite number of solutions

22. Various answers including:  A landlord had originally rented out his three apartments for a bit above $775 per month. Unfortunately the landlord had some significant medical bills from when he slipped on the ice outside his own building. Unfortunately for the tenants, the landlord took out his frustration on them by raising their monthly rent (r) according to the equation r – 150 > 775

23. x ≤ 128,