Printable practice for solving inequalities by division (positive coefficients)

📚 Topic Summary

Solving inequalities by division is very similar to solving regular equations. The main goal is to isolate the variable on one side of the inequality. When you divide both sides of an inequality by a positive number, the inequality sign stays the same. For example, if you have $2x > 6$, you can divide both sides by 2 to get $x > 3$. This principle is crucial for finding the range of values that satisfy the inequality.

🧠 Part A: Vocabulary

Match the term with its definition:

1. Term: Inequality
2. Term: Variable
3. Term: Coefficient
4. Term: Isolate
5. Term: Solution Set

1. Definition: A symbol representing an unknown value.
2. Definition: To set apart or separate from others.
3. Definition: A mathematical statement comparing two expressions using symbols like >, <, ≥, or ≤.
4. Definition: The number multiplied by a variable.
5. Definition: The set of all values that satisfy the inequality.

✍️ Part B: Fill in the Blanks

When solving inequalities by __________, the goal is to __________ the __________ on one side. If you divide both sides by a __________ number, the inequality sign remains the __________. The solution is the set of numbers that make the inequality __________.

🤔 Part C: Critical Thinking

Explain in your own words why it's important to remember the rule about flipping the inequality sign when dividing by a negative number (we didn't do it in this exercise because the coefficient is positive!). What happens if you forget to do it?