📚 Topic Summary
One-step inequalities are mathematical statements that compare two expressions using inequality symbols such as < (less than), > (greater than), $\leq$ (less than or equal to), and $\geq$ (greater than or equal to). Solving one-step inequalities involves isolating the variable using inverse operations, similar to solving one-step equations. However, a crucial difference is that when you multiply or divide both sides of an inequality by a negative number, you must reverse the direction of the inequality symbol. This activity sheet will help you practice and understand these concepts.
🧠 Part A: Vocabulary
Match each term with its definition.
| Term |
Definition |
| 1. Inequality |
A. A value that, when substituted for a variable, makes the inequality true. |
| 2. Solution Set |
B. A statement that compares two expressions using inequality symbols. |
| 3. Inverse Operation |
C. The set of all values that satisfy the inequality. |
| 4. Addition Property of Inequality |
D. Performing the opposite operation to isolate the variable. |
| 5. Multiplication Property of Inequality |
E. Adding the same number to both sides of an inequality preserves the inequality. |
|
F. Multiplying both sides of an inequality by the same positive number preserves the inequality; multiplying by a negative number reverses it. |
✏️ Part B: Fill in the Blanks
Complete the following sentences using the words provided: reverse, isolate, inequality, solution, negative.
- To solve an ________, we need to ________ the variable.
- When multiplying or dividing by a ________ number, we must ________ the inequality symbol.
- The ________ to an inequality is any value that makes the inequality true.
🤔 Part C: Critical Thinking
Explain in your own words why it is necessary to flip the inequality sign when multiplying or dividing by a negative number. Provide an example to illustrate your explanation.