📚 Topic Summary
Two-step inequalities build upon the basics of solving equations, but with a twist! Instead of finding a single value for a variable, we determine a range of values that satisfy the inequality. Remember to perform inverse operations (addition/subtraction, multiplication/division) to isolate the variable, and crucially, flip the inequality sign whenever you multiply or divide by a negative number. Mastering these skills is essential for more advanced algebra!
🧮 Part A: Vocabulary
Match the terms on the left with their definitions on the right.
| Term |
Definition |
| 1. Inequality |
A. A value that, when substituted for a variable, makes the inequality true. |
| 2. Solution Set |
B. The point at which two lines or curves intersect on a graph. |
| 3. Inverse Operation |
C. A mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥. |
| 4. Intersection |
D. An operation that undoes another operation (e.g., addition and subtraction). |
| 5. Variable |
E. A symbol (usually a letter) that represents an unknown quantity. |
✍️ Part B: Fill in the Blanks
Complete the following paragraph using the words: inequality, opposite, number, solution, sign.
Solving a two-step __________ is similar to solving a two-step equation. We use __________ operations to isolate the variable. However, if we multiply or divide by a negative __________, we must flip the __________ of the inequality. The answer represents a __________ set, meaning there are multiple values that make the statement true.
🤔 Part C: Critical Thinking
Explain in your own words why it's important to flip the inequality sign when multiplying or dividing by a negative number. Provide an example to illustrate your explanation.