Linear Inequalities and Regions
Linear inequalities define regions on the number plane. The boundary is a line, and the solution is the half-plane satisfying the inequality.
What You Need to Know
Key Concept Diagram
Draw the boundary line using the equation (solid if <= or >=, dashed if < or >)
Test a point (e.g. the origin) to determine which side to shade
The solution region is the shaded area satisfying the inequality
Systems of inequalities produce an intersection region (feasible region)
Key Vocabulary
Inequality
A mathematical statement using <, >, <=, or >= instead of =
Half-plane
The region on one side of a line in the coordinate plane
Boundary line
The line that separates the solution region from the non-solution region
Feasible region
The intersection of multiple inequality regions in a system
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
For the inequality y > 2x - 1, should the boundary line be solid or dashed?
Question 2
To determine which side to shade for y < x + 3, test the point (0, 0). Is 0 < 0 + 3?
Question 3
A system of two linear inequalities produces a solution that is:
Key Concepts Summary
- ●Draw the boundary line using the equation (solid if <= or >=, dashed if < or >)
- ●Test a point (e.g. the origin) to determine which side to shade
- ●The solution region is the shaded area satisfying the inequality
- ●Systems of inequalities produce an intersection region (feasible region)