Inequalities

2. For Bill’s birthday party, his parents will pay $35 for the cake plus $15 per person for catering expenses. They will spend at most a total of $300 for his party. The greatest integer in the solution set of one of the following inequalities gives the maximum number of people, p, who can attend the party. Which one?

Writing and Solving Inequalities

2020 December(D03) Math Question 2

Which of the following inequalities is equivalent to x + 8 ≥ 4x − 16?

2026 April(R4A) Math Question 3

7. The Newton High School girls’ softball team currently has a record of 8 wins, 5 losses, and 0 ties. What is the least number of its remaining 10 games the team must win to finish the season winning more than 50% of all the team’s games?

2020 December(D03) Math Question 7

8. The solution set of 2x + 4 —8 is the set of all real values of .v such that:

2018 April(A09) Math Question 8

8. The floor plan for an L-shaped storage building is shown below with distances marked in feet. What is the floor area of the building, in square feet? (Note: Walls in this building meet only at right angles.)

2017 December(A10) Math Question 8

8. Assume that a, b, and c are real numbers. If a > b, and (a + c) > (b + c), then what is true of c ?

2014 December(72G) Math Question 8

12. A new club wants to attract customers who are at least 18 but less than 30 years of age. One of the number lines below illustrates the range of ages, in years, of the customers the club wants to attract. Which number line is it?

2017 June(74C) Math Question 12

2019 December(C03) Math Question 12

2012 December(71A) Math Question 12

2010 June(68C) Math Question 12

13. Which of the following graphs shows the solution set for the inequality 6x – 5 ?

2013 June(71C) Math Question 13

2018 December(B05) Math Question 14

2013 April(71G) Math Question 17

2013 December(71E) Math Question 19

19. Which of the following ordered pairs in the standard (x,y) coordinate plane satisfies the system of inequalities below?

2017 June(74C) Math Question 19

2013 December(71E) Math Question 20

21. Which of the following inequalities is equivalent to 3 − 2x > 7 − x ?

2021 June(D06) Math Question 21

23. Given that x <= 4 and x + y >= 5, what is the LEAST value that y can have?

2015 June(73C) Math Question 23

A theater manager must decide what prices to charge for adult and child tickets for an upcoming show. Based on previous data, the manager expects that a total of 420 tickets will be sold and the adult-to-child ratio of the numbers of tickets sold will be 1:3. The manager is working with the given constraints: the adult ticket price must be no more than 1.7 times the child ticket price, and the total amount of money from ticket sales must be at least $2,100. Let A represent the adult ticket price in dollars. Let C represent the child ticket price in dollars. Which of the following systems of inequalities represents the given expectations and constraints?

2026 April(R4A) Math Question 24

2013 December(71E) Math Question 28

28. When the system of inequalities below is graphed in the standard (x,y) coordinate plane, one of the following graphs is that of the solution set of the system. Which graph?

2014 June(72C) Math Question 28

2019 December(C03) Math Question 29

2009 June(67C) Math Question 29

29. Which of the following inequalities is equivalent to —2x— 6y> 2y— 4 ?

2015 June(73C) Math Question 29

2009 December(68A) Math Question 30

2010 April(68G) Math Question 31

2010 June(68C) Math Question 34

2012 April(70G) Math Question 38

2012 June(70C) Math Question 39

40. For real numbers x and y such that 0 ≤ x ≤ 5 and y ≥ 9, the expression can have which of the following values?

Domain and Range

2021 December(E23) Math Question 40

2013 April(71G) Math Question 41

2012 June(70C) Math Question 45

47. A number line graph includes the points at real numbers a and b, as shown below. Which of the following inequalities expresses an interval that must include the product ab ?

Number Line

2021 December(E23) Math Question 47

2012 April(70G) Math Question 48

2020 July(C01) Math Question 48

49. Which of the following number line graphs is that of the solution set to the inequality —2x + 12 >= 20 ?

2014 April(71H) Math Question 49

2012 June(70C) Math Question 49

49. The shaded region in the graph below represents the solution set to which of the following systems of inequalities?

2014 June(72C) Math Question 49

52. One of the following inequalities is graphed below in the standard (x,y) coordinate plane. Which one?

2015 December(72E) Math Question 52

2012 June(70C) Math Question 53

55. ·The graph of y= x+1, y= x-3 and x2 + y2= 9 are
shown in the standard (x,y) coordinate plane below.
The, shaded region is the solution set to one o{ the
following systems of inequalities. Which system is it?

2019 June(B02) Math Question 55

2009 June(67C) Math Question 55

55. The shaded portion of the graph in the standard(x,y) coordinate plane below represents the solution set of one of the following systems of linear inequalities. Which one?

2015 June(73C) Math Question 55

2011 June(69F) Math Question 56

56. Each of the following graphs in the standard (x,5) DO YOUR FIGURING HERE.

2017 June(74C) Math Question 56

56. Which of the following graphs best represents the system of inequalities below?

2013 June(71C) Math Question 56

56. In one of the following graphs in the standard (x,y) coordinate plane, the solution set to the system of inequalities below is shown shaded. Which one? x + 2y ≤ 6 3x2 > 12 − 3y2

Graphing Circular Inequalities

Graphing Linear Inequalities

2021 April(Z04) Math Question 56

59. Let the values of real numbers a, b, and c be restricted by the 2 conditions given below.

InequalitiesThere are 50 ACT math questions under Inequalities

Sub-topics

2020 December(D03) Math Question 2

2026 April(R4A) Math Question 3