📚 Topic Summary
Graphing inequalities is a way to visually represent inequalities on a number line or coordinate plane. For Grade 7, we'll focus on graphing inequalities on a number line. An inequality compares two values, showing that one value is greater than, less than, greater than or equal to, or less than or equal to another value. The number line helps us see all the possible solutions that make the inequality true. For example, $x > 3$ means x can be any number greater than 3, which we represent with an open circle at 3 and a line extending to the right.
When graphing inequalities, remember that an open circle (o) means the number is not included in the solution (e.g., > or <), while a closed circle (●) means the number is included (e.g., ≥ or ≤).
🧮 Part A: Vocabulary
Match the term with its definition:
| Term |
Definition |
| 1. Inequality |
A. A visual representation of numbers on a line. |
| 2. Number Line |
B. A statement that compares two expressions using symbols like >, <, ≥, or ≤. |
| 3. Open Circle |
C. Indicates the number is included in the solution set. |
| 4. Closed Circle |
D. Indicates the number is NOT included in the solution set. |
| 5. Solution Set |
E. The set of all numbers that make the inequality true. |
✍️ Part B: Fill in the Blanks
Complete the following paragraph using the words: inequality, number line, open, closed, solutions.
Graphing an __________ helps us visualize the __________ to the problem. We use a __________ to represent all possible values. An __________ circle indicates that the endpoint is not included, while a __________ circle means it is included.
🤔 Part C: Critical Thinking
Explain in your own words why it is important to use an open or closed circle when graphing inequalities on a number line. Give an example to support your answer.