Real-world linear inequalities help us solve problems where the answer isn't just one number, but a range of numbers. Think about it: maybe you need to earn at least $50, or spend no more than $20. These "at least", "no more than", "greater than", or "less than" situations translate into inequalities. Instead of an equals sign ($=$), we use inequality symbols like $>$ (greater than), $<$ (less than), $\geq$ (greater than or equal to), or $\leq$ (less than or equal to). This quiz will help you translate word problems into these mathematical statements and solve them!
Let’s get started with some key terms and practice exercises!
Match the term with its correct definition:
| Term | Definition |
|---|---|
| 1. Inequality | A. A value that, when substituted for a variable, makes the inequality true. |
| 2. Variable | B. A symbol (usually a letter) that represents an unknown number. |
| 3. Solution Set | C. A mathematical sentence that compares two expressions using inequality symbols. |
| 4. Constant | D. A fixed value that does not change. |
| 5. Coefficient | E. A number multiplied by a variable in an algebraic expression. |
Match each term to its definition. For example: 1-C, 2-B, and so on.
Complete the paragraph below using the words provided:
Words: greater, less, equal, inequality, solutions
A linear __________ is a statement that shows a relationship between two expressions that are not __________. Unlike equations, which have one or more specific __________ (values that make the equation true), inequalities have a range of __________. The symbols used represent if one expression is __________ than or __________ than another.
Explain, in your own words, how to translate a real-world problem (like saving money) into a linear inequality. Give a specific example.
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