Graphing inequalities is a way to visually represent all the possible solutions to an inequality on a number line. Unlike equations that have a single solution, inequalities have a range of solutions. When graphing, remember to use open circles for inequalities with '<' or '>' (meaning 'less than' or 'greater than') and closed circles for inequalities with '$\leq$' or '$\geq$' (meaning 'less than or equal to' or 'greater than or equal to'). Also, the arrow indicates all the values that satisfy the inequality.
Match the terms with their definitions:
| Term | Definition |
|---|---|
| 1. Inequality | A. A circle on the number line that is not filled in. |
| 2. Solution Set | B. A mathematical statement that compares two expressions using symbols like <, >, $\leq$, or $\geq$. |
| 3. Closed Circle | C. All the values that make an inequality true. |
| 4. Open Circle | D. A circle on the number line that is filled in. |
| 5. Number Line | E. A line on which numbers are marked at intervals, used to illustrate numerical operations. |
Match the terms: 1-?, 2-?, 3-?, 4-?, 5-?
Complete the following paragraph using the words: greater, less, closed, open, inequality.
An ___________ compares two expressions. When graphing, we use an ___________ circle to represent '<' or '>', and a ___________ circle to represent '$\leq$' or '$\geq$'. The arrow shows numbers ___________ than or ___________ than the value.
Explain, in your own words, why it's important to use an open or closed circle when graphing inequalities. What does each type of circle represent about the solution set?
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