📚 Topic Summary
Two-step inequalities are like regular two-step equations, but instead of an equals sign (=), we use an inequality symbol ($>, <, \geq, \leq$). Solving them involves isolating the variable using inverse operations. Graphing the solution on a number line shows all the possible values that make the inequality true. Remember to use an open circle for $ > $ and $ < $ (not included) and a closed circle for $\geq$ and $\leq$ (included). The arrow shows all possible solutions.
🧮 Part A: Vocabulary
Match the term with its definition:
| Term |
Definition |
| 1. Inequality |
A. A line that shows the solutions to an inequality. |
| 2. Variable |
B. A symbol, usually a letter, that represents an unknown number. |
| 3. Solution Set |
C. A mathematical statement that compares two expressions using symbols like $>, <, \geq,$ or $\leq$. |
| 4. Open Circle |
D. All the values that make an inequality true. |
| 5. Number Line |
E. Used on a graph to show that the number is not included in the solution. |
✍️ Part B: Fill in the Blanks
Complete the following paragraph using the words: inequality, solution, variable, operations, number line.
Solving an __________ involves isolating the __________ by using inverse __________. The __________ represents all possible values for the solution. This __________ can be shown on a ___________.
🤔 Part C: Critical Thinking
Explain in your own words why it is important to reverse the inequality sign when multiplying or dividing by a negative number when solving inequalities. Give an example.