Open circle at 3 and shade left.
(−∞, 3)Free Interactive Algebra Tool
Inequalities & Interval Notation Practice
Practice graphing one-variable inequalities on a number line and converting between inequality notation, interval notation, and visual graphs.
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Review open and closed endpoints, shading direction, compound inequalities, infinity notation, and how number-line graphs connect to interval notation.
Read the Inequalities & Interval Notation Guide
Practice Mode
Choose how you want to practice inequalities.
Problem 1 of 10
10%
Current Problem
Find the endpoint, choose the endpoint type, then shade the correct region.
Graph Inequality
Beginner
Current Problem
x < 3
1
Endpoint
2
Open / Closed
3
Shade
Step 1
Place the endpoint
Click the correct value on the number line.
x < 3
Endpoint Type
Shade
Step 1
Read the endpoint
Identify the endpoint shown on the graph.
Step 1
Identify the endpoint
Determine which values form the boundaries of the interval.
x < 3
Step 1
Read the interval endpoints
Identify the boundary values and whether each endpoint is included.
(−∞, 3)
Start by identifying the endpoint.
Hint
A strict inequality uses an open circle.
Inequalities & Interval Notation Reference
Closed circle at 3 and shade left.
(−∞, 3]Open circle at 3 and shade right.
(3, ∞)Closed circle at 3 and shade right.
[3, ∞)Open at −2, closed at 5, shade between.
(−2, 5]Infinity is never included, so always use a parenthesis with ∞ or −∞.
Parentheses mean an endpoint is not included. Brackets mean a finite endpoint is included.
Problem Complete
(−∞, 3)
The inequality x < 3 uses an open endpoint at 3 and includes all values to the left.
Problems Solved
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Correct Steps
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Incorrect Attempts
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Practice Round Complete
Great work!
You completed all 10 inequality and interval notation problems.
Problems Solved
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Open vs. Closed Endpoints
Strict inequalities use open circles. Inequalities with “or equal to” use closed circles.
Shade the Solution Set
Less-than inequalities shade left. Greater-than inequalities shade right. Compound inequalities may shade between two endpoints.
Interval Notation
Parentheses represent excluded endpoints. Brackets represent included finite endpoints.
Example
Convert a compound inequality to interval notation
Consider the inequality −2 < x ≤ 5.
−2 < x ≤ 5
1
Left endpoint
−2 is not included → (
2
Right endpoint
5 is included → ]
3
Write the interval
(−2, 5]
The number-line graph has an open circle at −2, a closed circle at 5, and shading between the endpoints.
Practice Inequalities and Interval Notation Step by Step
One-variable inequalities can be represented in several equivalent ways: with inequality symbols, with a graph on a number line, and with interval notation.
This interactive tool helps students connect all three representations instead of memorizing separate rules.
Graph One-Variable Inequalities
Students practice locating boundary values, choosing open or closed endpoints, and shading the correct side of the number line.
Open and Closed Circles
An open circle means the endpoint is not part of the solution. A closed circle means the endpoint is included.
Write Inequalities From Graphs
Number-line graphs can be translated back into inequality notation by reading the endpoint type and shading direction.
Convert Inequalities to Interval Notation
Interval notation uses parentheses for excluded endpoints and brackets for included finite endpoints. Infinity always uses parentheses.
Compound Inequalities
Intermediate practice introduces bounded solution sets such as −3 < x ≤ 4, which graph between two endpoints and translate directly into interval notation.
Union Intervals
Advanced practice can include “or” inequalities such as x < −2 or x ≥ 5. These solution sets contain two separate regions and are written using the union symbol.
Three Difficulty Levels
Beginner problems focus on single inequalities with one endpoint. Intermediate problems add compound inequalities. Advanced problems introduce union intervals, infinity, all-real solutions, and no-solution cases.