📚 Topic Summary
Multi-step inequalities are like regular equations but with an inequality sign ($<, >, \le, \ge$). Solving them involves isolating the variable by performing operations on both sides. The key steps include distributing (multiplying a term across parentheses) and combining like terms (adding or subtracting terms with the same variable or constant). Remember, when multiplying or dividing by a negative number, you must flip the inequality sign!
For example, consider $2(x + 3) > 4x - 6$. First, distribute the 2: $2x + 6 > 4x - 6$. Then, combine like terms by moving all x terms to one side and constants to the other. This gives $-2x > -12$. Finally, divide by -2 (and flip the sign!): $x < 6$.
🔤 Part A: Vocabulary
Match the term with its definition:
| Term |
Definition |
| 1. Inequality |
a. Terms that have the same variable raised to the same power. |
| 2. Distributive Property |
b. A statement that compares two expressions using symbols like <, >, ≤, or ≥. |
| 3. Combining Like Terms |
c. The process of simplifying an expression by adding or subtracting like terms. |
| 4. Like Terms |
d. Multiplying a term by each term inside the parentheses. |
| 5. Solution Set |
e. The set of all values that make the inequality true. |
✍️ Part B: Fill in the Blanks
When solving multi-step inequalities, first use the ________ property to eliminate parentheses. Then, ________ like terms on each side of the inequality. Remember to ________ the inequality sign when multiplying or dividing by a ________ number. The ________ is the set of all values that satisfy the inequality.
🤔 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. Use an example to illustrate your explanation.