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Inequalities and Their Solutions

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

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

-5 and 5 are included in the solution

Q: Why is the solution of x² - 25 = 0 written as two intervals?

Values outside the -5 and 5 satisfy the inequality.

Mathematics

This quiz covers various aspects of inequalities, including quadratic inequalities, interval notation, set-builder notation, graphing inequalities, and identifying solutions. It tests the understanding of boundary points, inclusion/exclusion of endpoints, and the interpretation of different inequality symbols.

Inequalities Algebra Graphing

20 Questions Medium Ages 14+ Aug 28, 2026

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About this Study Set

This study set covers Mathematics through 20 practice questions. This quiz covers various aspects of inequalities, including quadratic inequalities, interval notation, set-builder notation, graphing inequalities, and identifying solutions. It tests the understanding of boundary points, inclusion/exclusion of endpoints, and the interpretation of different inequality symbols. 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 20 questions from the Inequalities and Their Solutions 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 (1, 2)
C (4, 3)
D (5, 0)

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

A Open circles at boundary points
B Closed circles at boundary points
C Arrows pointing outwards
D Dashed lines

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

A Values beyond both roots satisfy the inequality.
B Values between roots satisfy only the inequality.
C The inequality is only defined for positive values.
D The square root of the constant is an integer.

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

A Endpoints are included in the solution.
B Endpoints are excluded from the solution.
C The interval represents only integers.
D The interval is symmetric around zero.

5 Which values of x satisfy the condition x² - 25 < 0?

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

6 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 undefined at the endpoints.
D The roots are imaginary.

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 x = -3 or 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 below a line
D A 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 Only values greater than 8
D Only values less 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 equations.
D They both include the boundary points in their solutions.

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

A x - y = 16
B x² + y = 16
C x + y² = 16
D x² + y² = 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 strict
D Because the y-intercept is positive

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 represents only negative values
D The interval represents only positive values

18 Why is the solution of x² - 25 = 0 written as two intervals?

A Values outside the -5 and 5 satisfy the inequality.
B Values inside the -5 and 5 satisfy the inequality.
C The inequality is undefined at -5 and 5.
D The roots are equal.

19 Which notation is commonly used to describe solution sets of inequalities?

A Interval notation
B Scientific Notation
C Set-builder notation
D Standard notation

20 What are the solutions of x² - 64 ≥ 0?

A (-8, 8)
B (-∞, -8] U [8, ∞)
C [-8, 8]
D (-∞, -8) U (8, ∞)

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