Year 11 - Maths
Solving a linear inequality graphically
Inequalities
Study Hub
Study Guides
This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit, pupils extend their understanding of inequalities and consider a range of contextual inequalities and ways to find and represent their solutions.
Lesson Summary
You will learn to extend your thinking to a linear inequality with 2 variables and can show this can be solved graphically to find a solution set.
Key Notes
- A linear inequality involving two variables can be graphed
- A solid line indicates the solutions on the line are valid
- A dashed line indicates a strict inequality
- By testing points not on the line, you can determine the region that satisfies the inequality
- This region is the solution set
Vocabulary To Learn
- Region (inequalities): A region is an area that graphically represents the solutions to one or more inequalities. Every coordinate pair within the region satisfies the inequalities that define the region.
Common Mistakes To Avoid
- Thinking that x = 4 is a line parallel to the x axis and that y = 4 is parallel to the y axis.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A linear inequality involving two variables can be graphed. A solid line indicates the solutions on the line are valid.
2. Use this key word in a maths sentence and explain it clearly. 'Region (inequalities)'
A region is an area that graphically represents the solutions to one or more inequalities. Every coordinate pair within the region satisfies the inequalities that define the region. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Thinking that x = 4 is a line parallel to the x axis and that y = 4 is parallel to the y axis. Correction: Consider the points along the line. Writing valid coordinate pairs lets pupils identify which coordinate stays the same and which one changes.
More Lessons In This Unit
- A single solution set Study Guide
- Advanced problem solving with linear inequalities Study Guide
- Checking and securing understanding of simultaneous equations Study Guide
- Inequalities on number lines Study Guide
- Linear inequalities in context Study Guide
- Non-solutions to simultaneous linear equations Study Guide
- Problem solving with linear inequalities Study Guide
- Relating graphical solutions to algebraic solutions for inequalities Study Guide
- Solution set notation Study Guide
- Solving a set of linear inequalities graphically Study Guide
- Solving more complicated linear inequalities Study Guide
- Solving quadratic inequalities algebraically Study Guide
- Solving quadratic inequalities in one variable graphically Study Guide
- Solving simple linear inequalities Study Guide
Browse all guides in the Year 11 Maths guide library.