📚 Topic Summary
Inequalities are mathematical statements that compare two values, showing that one is greater than, less than, greater than or equal to, or less than or equal to the other. When we translate word problems into inequalities, we're essentially turning English sentences into mathematical expressions that describe a range of possible solutions rather than a single answer. This is particularly helpful when dealing with constraints or limitations.
For example, the statement "x is greater than 5" can be written as $x > 5$. Similarly, "y is less than or equal to 10" translates to $y \leq 10$. Writing inequalities from word problems involves identifying key phrases like "at least", "no more than", "minimum", and "maximum" and translating them into the appropriate inequality symbols.
🔤 Part A: Vocabulary
Match the term with its definition:
| Term |
Definition |
| 1. Inequality |
A. The lowest possible value. |
| 2. Variable |
B. A symbol representing an unknown quantity. |
| 3. At least |
C. A mathematical statement comparing two unequal values. |
| 4. No more than |
D. Not exceeding a certain quantity. |
| 5. Minimum |
E. Not less than a certain quantity. |
✍️ Part B: Fill in the Blanks
Complete the paragraph with the correct words:
When translating word problems into ________, it's important to identify the ________ and the key phrases. For example, if a problem states "a number is less than or equal to 15," you would use the symbol $\leq$. If it says "a value is greater than 7," you'd use the symbol ________. Recognizing these phrases and symbols allows you to accurately represent the problem using a mathematical ________.
🤔 Part C: Critical Thinking
Explain in your own words why inequalities are useful in real-life situations. Provide an example.