Graphing inequalities on a number line
Graphing Inequalities on a Number Line is a foundational Grade 7-8 algebra skill. Students learn to represent one-variable inequalities using open and closed circles and arrows on a number line, distinguishing between strict and non-strict inequalities. This skill connects symbolic algebra to visual representation.
Key Concepts
Property An inequality shows a range of possible values. Use an open circle to show a number is excluded (like with $<$ or $ $) and a solid, filled in circle to show a number is included (like with $\le$ or $\ge$). The shaded part of the number line represents the entire solution set of possible numbers.
Examples To graph $x 3$, place an open circle on 3 and shade the number line to the right. To graph $x \le 2$, place a solid circle on 2 and shade the number line to the left. To graph $1 < x \le 5$, place an open circle on 1, a solid circle on 5, and shade between them.
Explanation Think of it as a VIP party guest list! An open circle means that number didn't get an invite, but all the numbers nearby did. A solid circle means that number is the guest of honor and is definitely included! The shaded line is the dance floor where all the cool, invited numbers hang out.
Common Questions
How do you graph an inequality on a number line?
Use an open circle for strict inequalities (< or >) and a closed circle for non-strict inequalities (≤ or ≥), then draw an arrow in the direction of the solution set.
What is the difference between an open and closed circle on a number line?
An open circle means the endpoint is NOT included in the solution (strict inequality), while a closed circle means it IS included (non-strict inequality).
How do you graph x > 3 on a number line?
Place an open circle on 3, then draw an arrow pointing to the right to show all values greater than 3.
What does a number line inequality look like for x ≤ -2?
Place a closed circle on -2 and draw an arrow pointing to the left to show all values less than or equal to -2.
Why do we graph inequalities on a number line?
Graphing inequalities on a number line gives a visual picture of all possible solutions, making it easier to understand the range of values that satisfy the inequality.