Graphing Solutions to Inequalities on a Number Line
Graphing solutions to inequalities on a number line in Grade 8 Saxon Math Course 3 shows the set of all values that satisfy an inequality using open or closed circles and shaded rays or segments. Open circles represent strict inequalities (< or >) while closed circles represent inclusive inequalities (less than or equal to, greater than or equal to). Students graph single and compound inequality solutions to visualize solution sets.
Key Concepts
New Concept An inequality is a mathematical statement used to indicate a range of possible numbers. Letting $x$ represent a possible number, we write $$1 < x < 10$$ We read this as "$x$ is greater than 1 and less than 10." What’s next This card just sets the stage. Next, you’ll work through examples on solving inequalities and graphing their solutions on a number line.
Common Questions
How do you graph an inequality on a number line?
Place a circle at the boundary value. Use an open circle for strict inequalities (< or >) and a closed circle for inclusive inequalities. Shade the number line in the direction of the solution.
What is the difference between an open and closed circle on a number line?
An open circle means the boundary value is NOT included in the solution (strictly less or greater than). A closed circle means the boundary IS included (less than or equal to, greater than or equal to).
How do you graph x > 3 on a number line?
Draw an open circle at 3 (because x cannot equal 3) and shade the number line to the right, indicating all values greater than 3.
How do you graph a compound inequality like 2 < x less than or equal to 7?
Place an open circle at 2 and a closed circle at 7, then shade the segment between them to show all values greater than 2 and at most 7.
How does Saxon Math Course 3 teach graphing inequalities?
Saxon Math Course 3 connects algebraic inequality solving to graphical representation on number lines, asking students to both solve inequalities and sketch the solution set.