An 'or' inequality combines two inequalities with the condition that at least one of them must be true. The solution set includes all values that satisfy either inequality, or both. Graphically, this is represented by the union of the solution sets of the individual inequalities. Solving 'or' inequalities involves solving each inequality separately and then combining their solutions.
For example, consider the inequality $x < 3$ or $x > 5$. The solution includes all numbers less than 3, as well as all numbers greater than 5.
Match the term with its definition:
| Term | Definition |
|---|---|
| 1. Inequality | A. The point on a number line where an inequality changes direction. |
| 2. Solution Set | B. A mathematical statement showing the relationship between two expressions that are not equal. |
| 3. Compound Inequality | C. A set of values that satisfy the inequality. |
| 4. Union | D. A statement containing two or more inequalities that are connected by 'and' or 'or'. |
| 5. Critical Value | E. A set containing all elements of two or more sets. |
Answers: 1-B, 2-C, 3-D, 4-E, 5-A
An 'or' inequality is a type of ________ inequality. To solve it, you must solve ________ inequality separately. The solution is the ________ of the solutions of each individual inequality. This means a value is a solution if it satisfies ________ inequality.
Answers: compound, each, union, either
Explain, in your own words, how the solution set of an 'or' inequality differs from that of an 'and' inequality. Give an example to illustrate your explanation.
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