Inequalities

Inequality Expressions

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. 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

2019 December(C03) Math Question 12

2010 June(68C) Math Question 12

2018 December(B05) Math Question 14

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

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

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

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

2020 July(C01) Math Question 48

2012 June(70C) Math Question 49

2009 June(67C) Math Question 55

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

Inequality ExpressionsInequalitiesACT math questions

2020 December(D03) Math Question 2

2026 April(R4A) Math Question 3