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Mathematical Inequalities and Intervals Quiz

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

The endpoints satisfy the inequality

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

Because the boundary is not included

Mathematics

A quiz covering quadratic inequalities, interval notation, boundary conditions, and set-builder notation.

Algebra Inequalities Intervals

16 Questions Medium Ages 14+ Aug 28, 2026

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About this Study Set

This study set covers Mathematics through 16 practice questions. A quiz covering quadratic inequalities, interval notation, boundary conditions, and set-builder notation. Every question includes the correct answer so you can learn as you go — pick any format above to get started.

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Browse all 16 questions from the Mathematical Inequalities and Intervals Quiz study set below. Each question shows the correct answer — select a study format above to practice interactively.

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

A Open circles
B Closed circles
C Dashed lines
D Arrows

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

A Values between roots satisfy
B Values beyond both roots satisfy
C The parabola opens downward
D The vertex is at the origin

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

A Endpoints are excluded
B Endpoints are included
C The interval is infinite
D The values are negative

4 For the garden 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

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

A The endpoints are outside the graph
B The endpoints satisfy the inequality
C The inequality is greater than zero
D The boundary is excluded

6 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}

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

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

8 Which solution set satisfies x² - 9 < 0?

A x < -3 or x > 3
B -3 < x < 3
C x < 9
D x > 3

9 Which interval represents all values less than -2?

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

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

A A shaded region above a line
B A shaded region below a line
C A shaded region inside a circle
D A shaded region outside a parabola

11 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 greater than 64
D Values less than -8

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

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

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

A Their graphs have different vertices
B Their solution intervals are complementary
C Both have the same solution set
D Neither has a solution

14 Which equation forms the boundary of x² + y = 16?

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

15 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 slope is positive
D Because it is a quadratic equation

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

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

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