📚 Topic Summary
Linear inequality word problems involve translating real-world scenarios into mathematical inequalities and then solving them. Unlike equations which have a single solution, inequalities have a range of solutions. Key phrases like "at least," "no more than," "greater than," and "less than" indicate inequalities. Translating these phrases correctly is crucial for setting up the problem.
For example, if a problem states, "John needs to earn at least $50," you would translate "at least" to the inequality symbol $\geq$. The inequality would then be written as $E \geq 50$, where E represents the amount John earns.
🔤 Part A: Vocabulary
Match the terms with their definitions:
| Term |
Definition |
| 1. Inequality |
A. The point that divides the number line into solutions and non-solutions |
| 2. Variable |
B. A symbol representing an unknown quantity |
| 3. Solution Set |
C. A mathematical statement comparing two expressions using symbols like <, >, ≤, or ≥ |
| 4. Boundary Point |
D. All the values that satisfy the inequality |
| 5. Constraint |
E. A limitation or restriction on the possible values |
✍️ Part B: Fill in the Blanks
Complete the following paragraph using the words: greater, less, at least, no more than, solution.
When solving linear inequality word problems, it's important to identify the key phrases. "At least" means the value is ________ or equal to a certain number. "No more than" means the value is ________ or equal to a certain number. The ________ to an inequality is a range of values, not just one number. We can also use phrases like "__________ than" or "__________ than" to define the relationship between two expressions.
🤔 Part C: Critical Thinking
Explain, in your own words, how to determine which inequality symbol ($<, >, \leq, \geq$) to use when translating a word problem into a mathematical inequality. Give an example.