Graphing Inequality Solutions
Graph inequality solutions on a number line in Grade 9 algebra using open circles for strict inequalities and closed circles for inclusive inequalities, then shade the solution ray or segment.
Key Concepts
Property An open circle ($\circ$) on a graph means the number is not part of the solution (used for $<$ and $ $). A closed circle ($\bullet$) means the number is included in the solution (used for $\leq$ and $\geq$). Explanation Graphing an inequality is like drawing a treasure map for all possible answers! The circle is your starting point. Use a closed circle if the endpoint is a valid answer ($\geq, \leq$), like a locked treasure chest that includes the key. Use an open circle if it's just a boundary ($ , <$), like a landmark you can't stand on. Examples The solution $x 5$ is graphed with an open circle at 5 and an arrow pointing to the right, showing all numbers greater than 5 are solutions. The solution $y \leq 2$ is graphed with a closed circle at 2 and an arrow pointing to the left because 2 is a solution. The solution $z < 0$ is graphed with an open circle at 0 and an arrow pointing left, indicating that 0 itself is not a solution.
Common Questions
How do you graph a simple inequality on a number line?
Place an open circle at the boundary value for strict inequalities (< or >) or a closed circle for inclusive inequalities (≤ or ≥). Then shade the number line toward the values that satisfy the inequality.
What is the difference between an open and closed circle on a number line graph?
An open circle indicates the boundary point is NOT included in the solution. A closed (filled) circle indicates the boundary point IS included. For x > 3, use an open circle at 3. For x ≥ 3, use a closed circle at 3.
How do you graph a compound inequality on a number line?
For AND inequalities like -2 < x < 5, shade the segment between -2 and 5 with appropriate open/closed circles at both ends. For OR inequalities like x < -2 or x > 5, shade outward rays in both directions.