📚 Topic Summary
Two-step linear inequalities are mathematical expressions that combine inequality symbols (like <, >, ≤, ≥) with algebraic expressions requiring two operations to isolate the variable. Solving them involves using inverse operations to isolate the variable on one side of the inequality, similar to solving equations, but with an added rule: multiplying or dividing by a negative number flips the inequality sign. For example, $2x + 3 > 7$ is a two-step inequality. The solution represents a range of values rather than a single value.
🧠 Part A: Vocabulary
Match each 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 mathematical statement that compares two expressions using symbols like <, >, ≤, or ≥. |
| 3. Solution Set |
C. A symbol (usually a letter) that represents an unknown value. |
| 4. Coefficient |
D. The number multiplied by the variable in an algebraic expression. |
| 5. Constant |
E. A fixed value that does not change. |
✍️ Part B: Fill in the Blanks
Complete the following paragraph with the correct terms:
Solving two-step inequalities is similar to solving two-step ________. The goal is to ________ the ________ on one side of the inequality. Remember, if you multiply or divide by a ________ number, you must flip the ________ sign.
🤔 Part C: Critical Thinking
Explain in your own words why multiplying or dividing by a negative number requires flipping the inequality sign. Provide an example to support your explanation.