Printable activities for graphing inequalities Grade 6.

📚 What are Inequalities?

Inequalities are mathematical statements that compare two values, showing that one value is either greater than, less than, or not equal to another. Unlike equations which use an equals sign (=), inequalities use symbols like > (greater than), < (less than), ≥ (greater than or equal to), and ≤ (less than or equal to).

• 🔍 Greater Than (>): Indicates a value is larger than another. For example, $x > 5$ means 'x' is any number bigger than 5.
• 💡 Less Than (<): Indicates a value is smaller than another. For example, $x < 3$ means 'x' is any number smaller than 3.
• 📝 Greater Than or Equal To (≥): Indicates a value is larger than or equal to another. For example, $x ≥ 2$ means 'x' is any number bigger than or equal to 2.
• ✔️ Less Than or Equal To (≤): Indicates a value is smaller than or equal to another. For example, $x ≤ 7$ means 'x' is any number smaller than or equal to 7.

📜 A Brief History

The use of inequality symbols has evolved over time. While the concept of comparing quantities existed long before, the standardized symbols we use today were popularized in the 17th and 18th centuries. Mathematicians like Thomas Harriot played a key role in introducing and standardizing mathematical notation, including the inequality symbols. These symbols allowed for more concise and universal mathematical communication.

➗ Key Principles of Graphing Inequalities

Graphing inequalities on a number line helps visualize all possible solutions. Here are the key principles:

• 🟢 Number Line Setup: Draw a number line and mark relevant numbers.
• 🔵 Open Circle (O): Use an open circle on the number line for strict inequalities (> or <). This indicates the number itself is not included in the solution.
• ⚫ Closed Circle ( ): Use a closed (filled-in) circle for inequalities that include 'equal to' (≥ or ≤). This indicates the number is included in the solution.
• ➡️ Direction of Arrow: Draw an arrow to indicate all other values that satisfy the inequality. The arrow points to the right for 'greater than' and to the left for 'less than'.

🌍 Real-World Examples

Inequalities show up all the time in the real world. Let's explore a few examples:

• 🌡️ Temperature: The temperature must be greater than 20°C to go swimming: $T > 20$
• ⚖️ Weight Limit: The elevator can hold up to 500 kg: $W ≤ 500$
• ⏰ Time: You must be at least 12 years old to watch the movie: $A ≥ 12$

✏️ Graphing Inequalities Practice Quiz

Let's test your knowledge with these practice problems. For each inequality, draw the number line and graph the solution.

1. $x > 3$
2. $x ≤ -2$
3. $x ≥ 0$
4. $x < 5$
5. $x ≥ -1$
6. $x < -4$
7. $x ≤ 6$

(Answers: Number lines with appropriate circles and arrows indicating the solution sets for each inequality)

✅ Conclusion

Congratulations! You've learned the basics of graphing inequalities. With these skills, you're well-equipped to tackle more complex math problems and understand how inequalities apply in everyday situations. Keep practicing, and you'll become an inequality master in no time!