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Inequalities and Interval Notation Quiz
Mathematics
This quiz covers understanding and representing solutions to inequalities, including interval notation, set-builder notation, and number line graphs. It tests concepts like included/excluded endpoints, separate intervals, and graphical representations of inequalities.
Algebra
Inequalities
Graphing
33 Questions
Medium
Ages 14+
Aug 28, 2026
About this Study Set
This study set covers Mathematics through
33 practice questions.
This quiz covers understanding and representing solutions to inequalities, including interval notation, set-builder notation, and number line graphs. It tests concepts like included/excluded endpoints, separate intervals, and graphical representations of inequalities. Every question includes the correct answer so you can learn as you go — pick any format above to get started.
Questions & Answers
Browse all 33 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?
2
Which symbol indicates that endpoints are included in a number line solution?
-
A
Close circles at boundary points
-
B
Open circles at boundary points
3
Why does x² - 4 > 0 produce two separate intervals?
-
A
Values beyond both roots satisfy
-
B
Values between roots satisfy only
4
Why are brackets used in the interval [-3, 3]?
-
A
Endpoints are included in solution
-
B
Endpoints are excluded from solution
5
Which values of x satisfy the condition x² - 25 < 0?
-
A
x < -5 or x > 5
-
B
-5 < 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
7
Which set-builder notation represents (-3, 3)?
-
A
{x | -3 < x < 3}
-
B
{x | x < -3 or x > 3}
8
Which interval represents the solution of x² - 100 < 0?
9
Which solution set satisfies x² - 9 < 0?
-
A
-3 < x < 3
-
B
x < -3 or x > 3
10
Which interval represents all values less than -2?
11
Which graph represents the inequality y < x - 9?
-
A
A shaded region beside a line
-
B
A shaded region below a parabola
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
13
Which notation represents the set {x | x < -2}?
14
Which statement correctly compares x² - 16 < 0 and x² - 16 > 0?
-
A
Their solution intervals are complementary.
-
B
Their graphs have different vertices.
15
Which equation forms the boundary of x² + y² = 16?
-
A
x² + y² = 16
-
B
x - y = 16
16
Why is the boundary dashed for x + y < 9?
-
A
Because the boundary is not included.
-
B
Because the graph is always decreasing.
17
Why are brackets used in [-5, 5]?
-
A
-5 and 5 are included in the solution
-
B
-5 and 5 are excluded from the solution
18
Why are open circles used for x² - 9 > 0 at -3 and 3?
-
A
3 & -3 are excluded in the solution set
-
B
3 & -3 are included in the solution set
19
Why is shading used on a number line graph?
-
A
To indicate solution regions clearly
-
B
To indicate variable names clearly
20
Which student uses the correct reasoning when graphing x² + y > 16?
-
A
The boundary is dashed because equality is excluded.
-
B
The boundary is solid because equality is excluded.
21
Which interval notation represents all values between -5 and 5 without including the endpoints?
22
A drone may fly where x² + y < 18. Which point is permitted?
23
Which statement best describes x + 9 < 0?
-
A
Negative values satisfy inequality only
-
B
No real values satisfy inequality
24
A learner concludes that x² + 9 < 0 has solutions. How should this be evaluated?
-
A
Incorrect because no real solutions exist
-
B
Correct because negative values exist
25
Which number line graph represents the solution of x² - 9 < 0?
-
A
A graph with closed circles at -3 and 3, shaded between them.
-
B
A graph with open circles at -3 and 3, shaded between them.
26
A weather station uses x² + y ≤ 13. Which point represents an acceptable location?
27
Why does x² + 4 < 0 have no real solution?
-
A
Square values cannot produce negatives
-
B
Critical values are repeated roots
28
Which inequality has solution set (-4, 4)?
-
A
x² - 16 < 0
-
B
x² - 16 > 0
29
Which symbol indicates that endpoints are excluded from a number line solution?
-
A
Open circles at boundary points
-
B
Closed circles at boundary points
30
Which interval solves x² - 49 < 0?
-
A
(-7, 7)
-
B
(-∞, -7) U (7, ∞)
31
A student shades the interval (-7, 7) on a number line to represent x² - 49 > 0. What is the best evaluation of their graph?
-
A
Incorrect because the shaded regions should be outside the roots
-
B
Correct because the shaded region should be between the roots
32
Which of the following inequality symbols indicates that the endpoint values are included in the solution set?
33
Which notation expresses solutions of x² - 36 ≥ 0?
-
A
(-∞, -6] U [6, ∞)
-
B
(-6, 6)
