Solving And Graphing Inequalities

9.Write down the three inequalities that define the region R shown in the diagram. The region is above the dotted line y = x, below the solid line y = -x + 7, and to the right of the solid line x = 1.

10.A region is defined by the inequalities y ≤ 2, x < 3, and y ≤ x + 4. Which of the following points is NOT in the region?

11.Solve the inequality 2x + 3y ≤ 30 for y in terms of x.

12.A car hire company has x small cars and y large cars. The company has at least 6 cars total. The number of large cars is less than or equal to the number of small cars. The largest number of small cars is 8. Which set of inequalities represents this?

13.Klaus buys x silver balloons and y gold balloons. He buys more gold than silver, at least 15 silver, less than 50 gold, and total no more than 70. Which inequality is correct?

14.Given that x and y are integers such that 3 < x < 7, 4 < y < 9, and x + y = 13, find all possible values of x.

15.Which inequality represents the region to the left of the vertical line x = -2, including the line?

16.The shaded region on a graph is below the dotted line y = 2x and above the solid line y = -x + 3. Which inequalities define the region?

17.Klaus buys x silver balloons and y gold balloons. He buys more gold than silver, at least 15 silver, less than 50 gold, and total no more than 70. Which set of inequalities represents this?

18.A company makes x chairs and y tables. Each chair requires 2 hours of labour and each table requires 3 hours. The total labour available per week is at most 30 hours. They must make at least 4 chairs and at least 2 tables. Which set of inequalities represents these constraints?

19.The diagram shows a triangle with vertices at (0,0), (4,0), and (0,3). The shaded region is defined by three inequalities. Two of them are y ≥ 0 and x ≥ 0. What is the third inequality?

20.Which inequality represents the region to the left of the vertical line x = -1, not including the line?

21.A rectangular region is defined by the inequalities 1 ≤ x ≤ 5 and 2 ≤ y ≤ 6. Which of the following points lies inside the region?

22.Solve the inequality 2(x - 3) ≥ 5x + 4.

23.When graphing the inequality y > 3x - 2, the line y = 3x - 2 should be drawn as:

24.A region is defined by y ≥ x, y ≤ -x + 6, and y ≥ 0. Which of the following points is inside the region?

25.The diagram shows a circle with centre (0,0) and radius 5. The shaded region is inside the circle and above the x-axis. Which inequalities define the shaded region?

26.A car park has x spaces for cars and y spaces for vans. There are at most 50 spaces in total. The number of van spaces is at most half the number of car spaces. There are at least 10 car spaces. Which inequalities represent this?

27.Which inequality is represented by the solid line y = -2x + 5 and the region below it?

28.Given that x and y are integers such that -2 < x < 3 and 1 < y < 5, and x + y = 4, find all possible values of x.

29.The inequality x ≤ 4 is represented on a graph by a vertical line at x = 4. Which side is the wanted region?

30.Solve the inequality 4 - 3x > 7 + 2x.

31.A region is defined by y < 2x + 1 and y ≥ -x + 3. Which point satisfies both inequalities?

32.When graphing the inequality y > 2x - 1, the line y = 2x - 1 should be drawn as:

33.The inequality x ≥ 3 is represented on a graph by a vertical line at x = 3. The wanted region is:

34.A company makes x chairs and y tables. Each chair requires 2 hours of labour and each table requires 3 hours. The total labour available per week is at most 30 hours. Which inequality represents this constraint?

35.When graphing the inequality y < 2x + 3, how should the line y = 2x + 3 be drawn?

36.The inequality y ≥ 4x - 1 is represented by a solid line and the region below the line.

37.Which inequality describes the region to the left of the vertical line x = -3, including the line?

38.Which of the following points satisfy the inequality y ≤ 2x + 1? (Select all that apply)

39.Match each inequality to the correct description of its graph.

40.Put the following steps for graphing the inequality y ≥ 2x - 1 in the correct order.

41.The diagram shows a region defined by three inequalities. Two of the lines are x = 2 (solid) and y = x (dotted). The shaded region is below y = x and to the right of x = 2. Which of the following could be the third inequality?

42.A region is defined by y ≥ 0, x ≥ 0, and y ≤ -x + 4. Which of the following points lies inside the region?

43.Match each inequality with the correct description of its graph.

44.Which of the following points satisfy the inequality y ≥ 2x - 3? (Select all that apply)

45.Find the y-coordinate of the point where the line y = 3x - 2 crosses the y-axis. Use this to decide whether the point (0, -3) lies above or below the line. Enter 1 if above, 0 if below.

46.Complete the sentence: For the inequality y > 3x - 1, the line is drawn ______ and the region ______ the line is shaded.

47.Write down the three inequalities that define the region R which is above the dotted line y = x, below the solid line y = -x + 7, and to the right of the solid line x = 1.

48.Solve the inequality 2x + 5 > 3x - 1. Enter the value of x such that x < number.

49.Complete the sentence: For the inequality y ≤ 2x + 5, the line is drawn ______ and the region ______ the line is shaded.

50.Find the y-coordinate of the point where the line y = 3x - 2 crosses the y-axis. Use this to decide whether the point (0, -3) lies above or below the line. Enter 1 if above, 0 if below.

51.Solve the inequality 2x + 5 > 3x - 1. Enter the value of x such that x < number.