Given That − 5 \textless − 3 -5 \ \textless \ -3 − 5 \textless − 3 , Which Statement Is Not True?A. -3 Is To The Right Of -5 On The Number Line.B. − 3 \textgreater − 5 -3 \ \textgreater \ -5 − 3 \textgreater − 5 C. -5 Is To The Left Of -3 On The Number Line.D. -3 Is Less Than -5

Introduction

In mathematics, number lines are a fundamental tool for representing and comparing numbers. A number line is a visual representation of the set of real numbers, with each point on the line corresponding to a unique number. Understanding how to read and interpret number lines is crucial for solving various mathematical problems, including those involving inequalities. In this article, we will explore the relationship between number line representation and inequality statements, focusing on the given statement: $-5 \ \textless \ -3$. We will examine each option and determine which statement is not true.

Option A: -3 is to the right of -5 on the number line

When we say that -3 is to the right of -5 on the number line, we are referring to the relative position of these two numbers on the line. In a number line, the right side represents positive numbers, while the left side represents negative numbers. Since -3 is to the right of -5, it means that -3 is greater than -5. This statement is true because, on a number line, the point corresponding to -3 is indeed to the right of the point corresponding to -5.

Option B: $-3 \ \textgreater \ -5$

This statement is a mathematical expression of the inequality -3 > -5. In this context, the symbol ">" represents "greater than." Since we have established that -3 is to the right of -5 on the number line, it follows that -3 is indeed greater than -5. Therefore, this statement is also true.

Option C: -5 is to the left of -3 on the number line

This statement is a direct representation of the given inequality: $-5 \ \textless \ -3$. On a number line, the point corresponding to -5 is indeed to the left of the point corresponding to -3. This statement is true because it accurately reflects the relative position of these two numbers on the number line.

Option D: -3 is less than -5

This statement is a mathematical expression of the inequality -3 < -5. However, we have already established that -3 is greater than -5, not less than. This statement is false because it contradicts the given inequality: $-5 \ \textless \ -3$.

Conclusion

In conclusion, the statement that is not true is Option D: -3 is less than -5. This statement contradicts the given inequality: $-5 \ \textless \ -3$, which indicates that -5 is less than -3. Understanding number line representation and inequality statements is crucial for solving various mathematical problems, and this article has provided a clear explanation of the relationship between these concepts.

Key Takeaways

• Number lines are a fundamental tool for representing and comparing numbers.
• Understanding how to read and interpret number lines is crucial for solving various mathematical problems.
• Inequality statements can be represented on a number line, with the relative position of numbers indicating the direction of the inequality.
• The given inequality: $-5 \ \textless \ -3$ indicates that -5 is less than -3.

Additional Resources

For further practice and review, consider the following resources:

• Khan Academy: Number Lines and Inequalities
• Mathway: Number Line and Inequality Solver
• IXL: Number Line and Inequality Practice

Q: What is a number line?

A: A number line is a visual representation of the set of real numbers, with each point on the line corresponding to a unique number. It is a fundamental tool for representing and comparing numbers.

Q: How do I read a number line?

A: To read a number line, start at the origin (0) and move to the right to represent positive numbers, and move to the left to represent negative numbers. The distance between two points on the line represents the difference between the corresponding numbers.

Q: What is the relationship between number line representation and inequality statements?

A: Inequality statements can be represented on a number line, with the relative position of numbers indicating the direction of the inequality. For example, if -3 is to the right of -5 on the number line, it means that -3 is greater than -5.

Q: How do I determine the direction of an inequality on a number line?

A: To determine the direction of an inequality on a number line, follow these steps:

1. Identify the two numbers being compared.
2. Locate the points on the number line corresponding to these numbers.
3. Determine the relative position of the points, with the point corresponding to the larger number to the right of the point corresponding to the smaller number.

Q: What is the difference between < and > on a number line?

A: The symbol "<" represents "less than," while the symbol ">" represents "greater than." On a number line, "<" indicates that the point corresponding to the smaller number is to the left of the point corresponding to the larger number, while ">" indicates that the point corresponding to the larger number is to the right of the point corresponding to the smaller number.

Q: Can I use a number line to compare fractions?

A: Yes, you can use a number line to compare fractions. To do this, locate the points on the number line corresponding to the fractions being compared, and determine the relative position of the points.

Q: How do I use a number line to solve linear inequalities?

A: To use a number line to solve linear inequalities, follow these steps:

1. Write the inequality in the form ax + b < c or ax + b > c.
2. Locate the points on the number line corresponding to the values of x that satisfy the inequality.
3. Determine the relative position of the points, with the points corresponding to the values of x that satisfy the inequality to the right of the point corresponding to the value of x that does not satisfy the inequality.

Q: What are some common mistakes to avoid when using a number line?

A: Some common mistakes to avoid when using a number line include:

• Confusing the direction of the inequality.
• Failing to locate the points on the number line corresponding to the values being compared.
• Not considering the relative position of the points on the number line.

Q: How can I practice using a number line to compare numbers and solve inequalities?

A: You can practice using a number line to compare numbers and solve inequalities by:

• Creating number lines and labeling the points corresponding to different numbers and fractions.
• Using online resources, such as interactive number lines and inequality solvers.
• Practicing with sample problems and exercises.

By following these tips and practicing regularly, you will become more confident and proficient in using a number line to compare numbers and solve inequalities.