Graphing Inequalities on Number Lines and Grids
A free Pre-Algebra lesson from the “Coordinate Plane, Functions, and Slope” unit, with a worked example and practice problems including step-by-step solutions.
Inequality graphs show many solutions at once. On a number line, use an open circle for < or > and a closed circle for <= or >=. For simple two-variable inequalities, a boundary line separates the coordinate plane into regions. In Coordinate Plane, Functions, and Slope, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.
What you'll learn
- Graph one-variable inequalities on a number line
- Use open and closed boundary points
- Connect simple two-variable inequalities to shaded regions
Worked example
Problem. Describe the graph of x <= 4 on a number line.
- The symbol <= includes the boundary value.
- Use a closed circle at 4.
- Values less than 4 are to the left, so shade left.
- Connect the calculation back to Graphing Inequalities on Number Lines and Grids so the method, not just the arithmetic, is clear.
Answer: Closed circle at 4, shade left
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice and typed response). Counts include repeated prompts and variants.
Practice problems
1. How should x < 3 be graphed?
Choices: Open circle at 3, shade left · Closed circle at 3, shade left · Open circle at 3, shade right · Closed circle at 3, shade right
Show solution
- The symbol < does not include 3.
- Values less than 3 are to the left.
Answer: Open circle at 3, shade left
2. How should x >= -2 be graphed?
Choices: Open circle at -2, shade left · Closed circle at -2, shade right · Open circle at -2, shade right · Closed circle at -2, shade left
Show solution
- >= includes the boundary.
- Values greater than -2 are to the right.
Answer: Closed circle at -2, shade right
3. Which value satisfies x <= 5?
Choices: 6 · 5 · 8 · 10
Show solution
- Less than or equal includes 5.
- 5 satisfies x <= 5.
Answer: 5
4. How should x > 0 be graphed?
Choices: Open circle at 0, shade right · Closed circle at 0, shade right · Open circle at 0, shade left · Closed circle at 0, shade left
Show solution
- > does not include 0.
- Values greater than 0 are to the right.
Answer: Open circle at 0, shade right
5. Which inequality matches a closed circle at 7 shaded left?
Choices: x < 7 · x <= 7 · x > 7 · x >= 7
Show solution
- Closed circle means the boundary is included.
- Shading left means less than.
Answer: x <= 7
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