Procedure: Graphing an Inequality's Solution Set
Procedure: Graphing an Inequality Solution Set is a Grade 7 math skill in Big Ideas Math Advanced 2, Chapter 11: Inequalities, where students follow a step-by-step process to graph the solution set of a one-variable inequality on a number line: identifying the boundary value, choosing open or closed endpoint based on the inequality symbol, and shading in the correct direction to show all solutions.
Key Concepts
When graphing inequalities on a number line, we use different symbols to show whether the boundary point is included in the solution set. For strict inequalities like $x 3$ or $x < 3$, we use an open circle at the boundary point to show it is not included. For non strict inequalities like $x \geq 3$ or $x \leq 3$, we use a closed circle (or filled dot) at the boundary point to show it is included. We then shade the number line in the direction that contains all the solutions.
Common Questions
What are the steps for graphing an inequality solution set?
1. Solve the inequality for the variable. 2. Plot the boundary value on a number line with an open circle (for strict < or >) or a closed circle (for ≤ or ≥). 3. Shade the number line in the direction of the inequality (left for less than, right for greater than).
What is the difference between an open and closed circle on an inequality graph?
An open circle means the boundary value is NOT included in the solution (strict inequality). A closed (filled) circle means the boundary value IS included (non-strict inequality with ≤ or ≥).
How do you know which direction to shade?
Pick a test value on each side of the boundary and substitute it into the inequality. The side that makes the inequality true is the side to shade.
What is Big Ideas Math Advanced 2 Chapter 11 about?
Chapter 11 covers Inequalities, including writing, solving, and graphing one- and two-step inequalities, and identifying and correcting common solution errors.