Inequalities and Interval Notation Quiz

Q: Why does x² - 36 < 0 use closed circles at -6 and 6 on a number line?

The endpoints satisfy the inequality

Q: Why is the boundary dashed for x + y < 9?

Because the boundary is not included

Q: Why are brackets used in [-5, 5]?

-5 and 5 are included in the solution

Mathematics

This quiz covers understanding and representing solutions to various inequalities, including quadratic inequalities and those involving two variables, using interval notation, set-builder notation, and graphical representations. It also explores the meaning of open and closed circles/brackets on number lines and the concept of complementary solution sets.

Inequalities Interval Notation Algebra

17 Questions Medium Ages 14+ Aug 31, 2026

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About this Study Set

This study set covers Mathematics through 17 practice questions. This quiz covers understanding and representing solutions to various inequalities, including quadratic inequalities and those involving two variables, using interval notation, set-builder notation, and graphical representations. It also explores the meaning of open and closed circles/brackets on number lines and the concept of complementary solution sets. Every question includes the correct answer so you can learn as you go — pick any format above to get started.

Questions & Answers

Browse all 17 questions from the Inequalities and Interval Notation Quiz study set below. Each question shows the correct answer — select a study format above to practice interactively.

1 Which point satisfies x² + y² ≤ 16?

A (3, 4)
B (5, 0)
C (0, 5)
D (4, 4)

2 Which symbol indicates that endpoints are included in a number line solution?

A Open circles at boundary points
B Close circles at boundary points
C Parentheses
D Dashed lines

3 Why does x² - 4 > 0 produce two separate intervals?

A Values between roots satisfy
B Values beyond both roots satisfy
C Endpoints are excluded from solution
D Endpoints are included in solution

4 Why are brackets used in the interval [-3, 3]?

A Endpoints are excluded from solution
B Endpoints are included in solution
C The interval represents only integers
D The interval is infinite

5 A square garden's area is limited by x² - 25 < 0. Which values of x satisfy the condition?

A x < -5 or x > 5
B -5 < x < 5
C x ≤ -5 or x ≥ 5
D -5 ≤ x ≤ 5

6 Why does x² - 36 < 0 use closed circles at -6 and 6 on a number line?

A The endpoints are outside the graph
B The endpoints satisfy the inequality
C The inequality is strict
D The inequality involves absolute value

7 Which set-builder notation represents (-3, 3)?

A {x | -3 < x < 3}
B {x | x < -3 or x > 3}
C {x | -3 ≤ x ≤ 3}
D {x | x ≤ -3 or x ≥ 3}

8 Which interval represents the solution of x² - 100 < 0?

A (-10, 10]
B (-10, 10)
C [-10, 10]
D (-∞, -10) U (10, ∞)

9 Which solution set satisfies x² - 9 < 0?

A x < -3 or x > 3
B -3 < x < 3
C x ≤ -3 or x ≥ 3
D -3 ≤ x ≤ 3

10 Which interval represents all values less than -2?

A [-2, ∞)
B (-∞, -2)
C (-∞, -2]
D (-2, ∞)

11 Which graph represents the inequality y < x - 9?

A A shaded region beside a line
B A shaded region below a parabola
C A shaded region above a line
D A shaded region below a line

12 A bridge remains stable when x² - 64 < 0. Which interval represents stability?

A Values from -8 through 8
B Values beyond -8 and 8
C Values less than -8
D Values greater than 8

13 Which notation represents the set {x | x < -2}?

A (-∞, -2]
B (-∞, -2)
C [-2, ∞)
D (-2, ∞)

14 Which statement correctly compares x² - 16 < 0 and x² - 16 > 0?

A Their graphs have different vertices.
B Their solution intervals are complementary.
C They have the same boundary points.
D They are equivalent inequalities.

15 Which equation forms the boundary of x² + y² ≤ 16?

A x - y = 16
B x² + y² = 16
C x + y = 16
D x² + y = 16

16 Why is the boundary dashed for x + y < 9?

A Because the graph is always decreasing
B Because the boundary is not included
C Because the inequality is greater than
D Because the inequality involves absolute value

17 Why are brackets used in [-5, 5]?

A -5 and 5 are excluded from the solution
B -5 and 5 are included in the solution
C The interval is infinite
D The interval represents only integers

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