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Inequalities and Intervals Quiz

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

The endpoints satisfy the inequality

Mathematics

A collection of practice questions covering quadratic inequalities, interval notation, and boundary conditions.

Algebra Inequalities Intervals

17 Questions Medium Ages 14+ Sep 2, 2026

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About this Study Set

This study set covers Mathematics through 17 practice questions. A collection of practice questions covering quadratic inequalities, interval notation, and boundary conditions. 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 Intervals Quiz study set below. Each question shows the correct answer — select a study format above to practice interactively.

1 Which point satisfies x² + y ≤ 10?

A (3,4)
B (2,5)
C (4,3)
D (1,1)

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

A Open circles
B Closed circles
C Dashed lines
D Arrows

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

A Values between roots satisfy
B Values beyond both roots satisfy
C Roots are excluded
D Inequality is linear

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

A Endpoints are excluded
B Endpoints are included
C Values are negative
D Values are positive

5 For the inequality x² - 25 < 0, which values of x satisfy the condition?

A x < -5 or x > 5
B -5 < x < 5
C x > 25
D x < -25

6 Why does x² - 36 < 0 use closed circles at -6 and 6?

A The endpoints satisfy the inequality
B The endpoints are outside the graph
C The roots are imaginary
D The inequality is greater than

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

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

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

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

9 Which solution set satisfies x² - 9 < 0?

A x < -3 or x > 3
B -3 < x < 3
C x < 9
D 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 Shaded region below a parabola
B Shaded region beside a line
C Shaded region inside a circle
D Shaded region above 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 x > 64
D x < -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 They have the same vertices
B Their solution intervals are complementary
C Both include the endpoints
D Both are linear

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

A x - y = 16
B x² + y = 16
C x + y² = 16
D x + y = 4

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

A The graph is decreasing
B The boundary is not included
C The inequality is quadratic
D The points are negative

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

A -5 and 5 are excluded
B -5 and 5 are included
C The interval is infinite
D The values are complex

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