📚 Topic Summary
Inequalities are mathematical statements that compare two values using symbols like < (less than), > (greater than), $\leq$ (less than or equal to), and $\geq$ (greater than or equal to). When we represent inequalities on a number line, we use open circles for < and > (because the endpoint isn't included) and closed circles for $\leq$ and $\geq$ (because the endpoint *is* included). The direction of the arrow indicates all the values that satisfy the inequality.
For example, if a number line shows a closed circle at 3 and an arrow pointing to the right, it represents the inequality $x \geq 3$. This means $x$ can be 3 or any number greater than 3.
🗂️ Part A: Vocabulary
Match the term with its definition:
| Term |
Definition |
| 1. Inequality |
A. A graph that represents all solutions to an inequality. |
| 2. Number Line |
B. A statement that compares two expressions using symbols like <, >, $\leq$, or $\geq$. |
| 3. Open Circle |
C. Indicates the endpoint is NOT included in the solution set of an inequality. |
| 4. Closed Circle |
D. A line on which numbers are marked at intervals, used to illustrate numerical relationships. |
| 5. Graph of Inequality |
E. Indicates the endpoint IS included in the solution set of an inequality. |
✍️ Part B: Fill in the Blanks
An _________ is a statement that compares two expressions using symbols like < and >. On a number line, a(n) _________ circle indicates that the endpoint is not included in the solution, while a(n) _________ circle shows that it is included. The _________ of the arrow on the number line tells us which values satisfy the inequality. For example, $x \leq 5$ means x is _________ than or equal to 5.
🤔 Part C: Critical Thinking
Explain how a number line helps you visualize the solutions to an inequality. Give an example of an inequality and how it would be represented on a number line.