Graphing Inequalities on a Number Line Calculator
Graph linear inequalities and compound inequality systems on a number line with interval notation
Graph Inequalities on Number Line
Inequality
Solution and Graph
Number Line Graph
• Open circles: not included in solution (<, >)
• Colored lines show the direction and range of each inequality
Example: Compound Inequality
Problem: Graph x > -2 and x ≤ 5
Step 1: We have two inequalities:
• x > -2 (greater than -2, open circle)
• x ≤ 5 (less than or equal to 5, filled circle)
Step 2: Find intersection of both conditions
Step 3: Values must satisfy both: x > -2 AND x ≤ 5
Solution
Answer: -2 < x ≤ 5
Interval Notation: (-2, 5]
Graph: Open circle at -2, filled circle at 5, line connecting them
Inequality Symbols
Less than
Open circle, strict inequality
Less than or equal to
Filled circle, non-strict
Greater than
Open circle, strict inequality
Greater than or equal to
Filled circle, non-strict
Interval Notation
[a, b]
Closed: includes endpoints
(a, b)
Open: excludes endpoints
[a, b)
Half-open: includes a, excludes b
(-∞, a]
Unbounded left, includes a
[a, ∞)
Unbounded right, includes a
∅
Empty set (no solution)
Understanding Inequality Graphing
What are Linear Inequalities?
Linear inequalities are mathematical expressions that compare a variable to a value using inequality symbols (<, ≤, >, ≥). Unlike equations that have specific solutions, inequalities represent ranges of values.
Compound Inequalities
- •AND: All inequalities must be satisfied simultaneously
- •Intersection: Find the overlap of all solution sets
- •No Solution: When inequalities contradict each other
Graphing Rules
Step 1: Mark the Point
Find the inequality value on the number line
Step 2: Choose Circle Type
Open circle for <, > | Filled circle for ≤, ≥
Step 3: Draw Direction
Left for <, ≤ | Right for >, ≥
Step 4: Find Intersection
Where all inequality regions overlap