Chapter 1
Linear Equations and Graphing
Course: Gre
Subject: Gre Quantitative Reasoning
Chapter: Inequalities And Absolute Values
One-Variable Inequalities on a Number Line
Steps:
- Solve the inequality for the variable
- Plot the boundary point(s) on a number line
Use an open circle for < or > Use a filled circle for ≤ or ≥
- Use an open circle for < or >
- Use a filled circle for ≤ or ≥
- Draw a ray or segment to show the solution region
Shade left for less than, right for greater than
- Shade left for less than, right for greater than
Example: Solve and graph 2x + 3 < 7
Solve: 2x < 4 → x < 2
Graph: Open circle at 2, arrow pointing left.
Two-Variable Inequalities on a Coordinate Plane
Steps:
- Solve the inequality for y (or leave in standard form)
- Graph the boundary line (replace inequality with equals sign)
Use a dashed line for < or > Use a solid line for ≤ or ≥
- Use a dashed line for < or >
- Use a solid line for ≤ or ≥
- Test a point (such as the origin) to determine which side to shade
- Shade the region that satisfies the inequality