Use An Inequality Symbol $(\ \textless \ , \ \textgreater \ , =, \leq$\] To Compare $-3 + 7$ And $-10 - 2$.A. $=$ B. $\ \textless \ $ C. $\ \textgreater \ $ D. $\leq$

Introduction

In mathematics, inequality symbols are used to compare two expressions and determine their relative values. In this discussion, we will explore how to compare the expressions $-3 + 7$ and $-10 - 2$ using inequality symbols. We will examine each option and determine which one is the correct comparison.

Understanding Inequality Symbols

Before we begin, let's review the inequality symbols used in this discussion:

• Less than ($\textless$): This symbol indicates that the value on the left is less than the value on the right.
• Greater than ($\textgreater$): This symbol indicates that the value on the left is greater than the value on the right.
• Equal to ($=$): This symbol indicates that the values on both sides are equal.
• Less than or equal to ($\leq$): This symbol indicates that the value on the left is less than or equal to the value on the right.

Comparing $-3 + 7$ and $-10 - 2$

Now that we have reviewed the inequality symbols, let's compare the expressions $-3 + 7$ and $-10 - 2$.

Evaluating $-3 + 7$

To evaluate the expression $-3 + 7$, we need to add $-3$ and $7$. When we add a negative number and a positive number, we need to consider the sign of the result.

result = -3 + 7
print(result)

The result of the expression $-3 + 7$ is $4$.

Evaluating $-10 - 2$

To evaluate the expression $-10 - 2$, we need to subtract $2$ from $-10$. When we subtract a positive number from a negative number, we need to consider the sign of the result.

result = -10 - 2
print(result)

The result of the expression $-10 - 2$ is $-12$.

Comparing the Results

Now that we have evaluated both expressions, let's compare the results.

• The result of $-3 + 7$ is $4$.
• The result of $-10 - 2$ is $-12$.

Since $4$ is greater than $-12$, we can conclude that $-3 + 7$ is greater than $-10 - 2$.

Conclusion

In conclusion, the correct comparison between $-3 + 7$ and $-10 - 2$ is:

• $-3 + 7$ is greater than $-10 - 2$.

Therefore, the correct answer is:

• C. $\textgreater$

Answer Key

• A. $=$: Incorrect
• B. $\textless$: Incorrect
• C. $\textgreater$: Correct
• D. $\leq$: Incorrect

Final Thoughts

Q: What is the difference between $\textless$ and $\textgreater$?

A: The symbols $\textless$ and $\textgreater$ are used to compare two expressions and determine their relative values. The symbol $\textless$ indicates that the value on the left is less than the value on the right, while the symbol $\textgreater$ indicates that the value on the left is greater than the value on the right.

Q: How do I evaluate an expression with a negative number and a positive number?

A: When evaluating an expression with a negative number and a positive number, you need to consider the sign of the result. If the result is positive, the expression is greater than zero. If the result is negative, the expression is less than zero.

Q: What is the difference between $\leq$ and $\textless$?

A: The symbols $\leq$ and $\textless$ are used to compare two expressions and determine their relative values. The symbol $\leq$ indicates that the value on the left is less than or equal to the value on the right, while the symbol $\textless$ indicates that the value on the left is strictly less than the value on the right.

Q: How do I compare two expressions with different signs?

A: When comparing two expressions with different signs, you need to consider the sign of the result. If the result is positive, the expression with the positive sign is greater than the expression with the negative sign. If the result is negative, the expression with the negative sign is greater than the expression with the positive sign.

Q: What is the correct order of operations when comparing expressions?

A: The correct order of operations when comparing expressions is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I determine the correct inequality symbol to use?

A: To determine the correct inequality symbol to use, you need to compare the values of the two expressions. If the value on the left is less than the value on the right, use the symbol $\textless$. If the value on the left is greater than the value on the right, use the symbol $\textgreater$. If the values are equal, use the symbol $=$. If the value on the left is less than or equal to the value on the right, use the symbol $\leq$.

Q: What are some common mistakes to avoid when comparing expressions?

A: Some common mistakes to avoid when comparing expressions include:

• Not evaluating expressions inside parentheses first.
• Not following the correct order of operations.
• Not considering the sign of the result.
• Not using the correct inequality symbol.

Q: How do I practice comparing expressions?

A: To practice comparing expressions, try the following:

• Start with simple expressions and gradually move on to more complex ones.
• Use a calculator or a computer program to evaluate expressions and compare their values.
• Practice comparing expressions with different signs and operations.
• Review and practice regularly to build your skills and confidence.

Conclusion

Comparing expressions is an important concept in mathematics, and it requires attention to detail and a clear understanding of the rules of operations. By following the correct order of operations and using the correct inequality symbols, you can accurately compare expressions and solve problems with confidence.