When to flip the inequality sign vs when not to Grade 7

📚 Understanding Inequality Signs

Inequalities are mathematical statements that compare two expressions using symbols like < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to). The big question is: when do you need to flip the sign?

🧮 Definition of 'Flipping the Sign'

Flipping the sign means changing the direction of the inequality. For example, if you start with $x < 5$, flipping the sign would result in $x > 5$. This happens in specific situations to maintain the truth of the inequality.

⚖️ Definition of 'Not Flipping the Sign'

Not flipping the sign means keeping the direction of the inequality the same. This is the more common scenario and applies in many algebraic manipulations.

📊 Comparison Table: Flipping vs. Not Flipping

🔑 Key Takeaways

• ➖ Multiplying/Dividing by Negatives: 🧪 When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign. This is crucial for maintaining the truth of the statement. For example: If $-x < 5$, then $x > -5$.
• ➕ Adding/Subtracting: ➕ When you add or subtract the same number from both sides, the inequality sign does not flip. For example: If $x - 3 > 2$, then $x > 5$.
• ➗ Multiplying/Dividing by Positives: ➗ When multiplying or dividing by a positive number, the inequality sign does not flip. For example: If $2x < 10$, then $x < 5$.
• 💡 Thinking it Through: 💡 Always consider what the operation is doing to the value of the variable. Does it require a change in direction to keep the statement true?
• 📝 Practice: 📝 The best way to master this is through practice! Try solving different inequalities to build your understanding.