Representing the Relationship with Symbols

Oct 13, 2025 by miodeya.com 101 views

In this scenario, we are given that Leticia spends $$18.45$

Defining the Inequality

Let $h$ represent the amount Humberto spends. Since Leticia spends at least $\$3.00$ more than Humberto, we can express this relationship as an inequality. The inequality will be in the form of $h \leq x$ , where $x$ is the amount Leticia spends.

Representing the Relationship with Symbols

To represent the relationship between Leticia and Humberto's spending, we need to use a symbol that indicates "less than or equal to." This symbol is $\leq$ . Therefore, the completed inequality will be $h \leq 18.45 - 3.00$ .

Simplifying the Inequality

To simplify the inequality, we need to subtract $3.00$ from $18.45$ . This will give us the amount that Humberto spends.

$h \leq 18.45 - 3.00$ $h \leq 15.45$

Conclusion

Key Takeaways

The inequality $h \leq 18.45 - 3.00$ represents the relationship between Leticia and Humberto's spending.
The symbol $\leq$ indicates "less than or equal to."
Humberto spends less than or equal to $\$15.45$ .

Real-World Applications

This scenario can be applied to real-world situations where we need to compare the spending of two individuals. For example, in a business setting, we may need to compare the expenses of two departments. In this case, we can use the same inequality to represent the relationship between the expenses of the two departments.

Common Mistakes to Avoid

When working with inequalities, it's essential to remember that the symbol $\leq$ indicates "less than or equal to." This means that the value on the left-hand side of the inequality can be equal to the value on the right-hand side. For example, in the inequality $h \leq 15.45$ , the value of $h$ can be equal to $15.45$ .

Tips for Solving Inequalities

When solving inequalities, it's essential to follow the order of operations. This means that we need to perform the operations inside the parentheses first, followed by the operations outside the parentheses. For example, in the inequality $h \leq 18.45 - 3.00$ , we need to subtract $3.00$ from $18.45$ before we can simplify the inequality.

Conclusion

In conclusion, the symbol that can be used to complete the inequality to represent the relationship between Leticia and Humberto's spending is $\leq$ . This symbol indicates that Humberto spends less than or equal to $\$15.45$ . By following the order of operations and using the correct symbol, we can solve inequalities and represent real-world relationships.

Frequently Asked Questions

Q: What is the symbol that can be used to complete the inequality to represent the relationship between Leticia and Humberto's spending?

A: The symbol that can be used to complete the inequality is $\leq$ .

Q: What does the symbol $\leq$ indicate?

A: The symbol $\leq$ indicates "less than or equal to."

Q: How can we simplify the inequality $h \leq 18.45 - 3.00$ ?

A: We can simplify the inequality by subtracting $3.00$ from $18.45$ . This will give us the amount that Humberto spends.

Q: What is the amount that Humberto spends?

A: The amount that Humberto spends is $\$15.45$ .

Q: How can we apply this scenario to real-world situations?

A: We can apply this scenario to real-world situations where we need to compare the spending of two individuals. For example, in a business setting, we may need to compare the expenses of two departments.

Q: What are some common mistakes to avoid when working with inequalities?

In the previous article, we discussed the relationship between Leticia and Humberto's spending and how to represent it using an inequality. In this article, we will answer some frequently asked questions about inequalities and relationships.

Q: What is an inequality?

A: An inequality is a mathematical statement that compares two values using a symbol such as $\leq$ , $\geq$ , $<$ , or $>$ .

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

A: The symbol $\leq$ indicates "less than or equal to," while the symbol $<$ indicates "less than." For example, the inequality $h \leq 15.45$ means that $h$ is less than or equal to $15.45$ , while the inequality $h < 15.45$ means that $h$ is strictly less than $15.45$ .

Q: How can I determine which symbol to use in an inequality?

A: To determine which symbol to use in an inequality, you need to consider the relationship between the two values being compared. If the value on the left-hand side of the inequality can be equal to the value on the right-hand side, use the symbol $\leq$ or $\geq$ . If the value on the left-hand side cannot be equal to the value on the right-hand side, use the symbol $<$ or $>$ .

Q: How can I simplify an inequality?

A: To simplify an inequality, you need to perform the operations inside the parentheses first, followed by the operations outside the parentheses. For example, in the inequality $h \leq 18.45 - 3.00$ , you need to subtract $3.00$ from $18.45$ before you can simplify the inequality.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when simplifying an expression or inequality. The order of operations is:

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

Q: How can I apply inequalities to real-world situations?

A: Inequalities can be applied to a wide range of real-world situations, such as:

Comparing the expenses of two departments in a business
Determining the maximum or minimum value of a variable
Modeling real-world relationships, such as the relationship between the price of a product and the quantity demanded

Q: What are some common mistakes to avoid when working with inequalities?

A: Some common mistakes to avoid when working with inequalities include:

Forgetting to follow the order of operations
Using the wrong symbol (e.g., using $\leq$ instead of $<$ )
Not considering the relationship between the two values being compared

Q: How can I practice solving inequalities?

A: You can practice solving inequalities by working through examples and exercises in a textbook or online resource. You can also try creating your own inequalities and solving them to practice your skills.

Conclusion

In conclusion, inequalities are a powerful tool for modeling real-world relationships and comparing values. By understanding the different symbols and how to simplify inequalities, you can apply inequalities to a wide range of situations. Remember to follow the order of operations and consider the relationship between the two values being compared to avoid common mistakes. With practice, you can become proficient in solving inequalities and apply them to real-world situations.