One-step inequality word problems involve translating real-world scenarios into mathematical inequalities that can be solved using a single operation (addition, subtraction, multiplication, or division). The key is to identify the unknown variable, the inequality symbol (>, <, ≥, ≤), and the relationship between the variable and the given numbers. Once you have the inequality, solve it just like you would solve a one-step equation, remembering to flip the inequality sign if you multiply or divide by a negative number. Let's practice!
Match the following terms with their definitions:
| Term | Definition |
|---|---|
| 1. Inequality | A. A value that, when substituted for a variable, makes the inequality true. |
| 2. Variable | B. A mathematical sentence showing a relationship other than equality. |
| 3. Solution Set | C. A symbol representing an unknown quantity. |
| 4. Greater Than | D. A symbol (>) indicating one value is larger than another. |
| 5. Less Than or Equal To | E. A symbol (≤) indicating one value is smaller than or equal to another. |
(Match the numbers 1-5 to the letters A-E)
An inequality uses symbols like ______, ______, ≥, and ≤ to show a relationship between two values. Solving an inequality is similar to solving an ______, but you must remember to ______ the inequality sign if you multiply or divide by a ______ number. The ______ of an inequality is the set of all numbers that make the inequality true.
Explain, in your own words, why it's important to flip the inequality sign when multiplying or dividing both sides of an inequality by a negative number. Provide an example to illustrate your explanation.
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