Determining the Correct Inequality

Oct 13, 2025 by magicalceylontours.com 39 views

As a prospective editor at a textbook company, it's essential to understand the average starting salary and the range of possible salaries. The average starting salary for an editor at a textbook company is $\$39,800$ , and the actual salaries can vary by less than $\$1,300$ . This means that the lowest possible salary is $\$39,800 - \$1,300 = \$38,500$ , and the highest possible salary is $\$39,800 + \$1,300 = \$41,100$ .

Determining the Correct Inequality

To determine whether a salary, $x$ , falls within the range of possible salaries, we need to use an inequality. The inequality should represent the range of possible salaries, which is between $\$38,500$ and $\$41,100$ . We can use the following inequality to determine whether a salary, $x$ , falls within this range:

Inequality: $38,500 \leq x \leq 41,100$

Breaking Down the Inequality

Let's break down the inequality and understand what it represents.

Lower Bound: $38,500 \leq x$
Upper Bound: $x \leq 41,100$

The lower bound represents the minimum salary, which is $\$38,500$ . Any salary that is greater than or equal to this amount will satisfy the lower bound.

The upper bound represents the maximum salary, which is $\$41,100$ . Any salary that is less than or equal to this amount will satisfy the upper bound.

Solving the Inequality

To solve the inequality, we need to find the values of $x$ that satisfy both the lower and upper bounds.

Lower Bound: $38,500 \leq x$
Upper Bound: $x \leq 41,100$

We can combine the two inequalities by using the "and" operator:

$38,500 \leq x \leq 41,100$

This inequality represents the range of possible salaries, which is between $\$38,500$ and $\$41,100$ .

Example

Suppose we want to determine whether a salary of $\$40,000$ falls within the range of possible salaries.

Lower Bound: $38,500 \leq 40,000$
Upper Bound: $40,000 \leq 41,100$

Since both the lower and upper bounds are satisfied, the salary of $\$40,000$ falls within the range of possible salaries.

Conclusion

In conclusion, the correct inequality to determine whether a salary, $x$ , falls within the range of possible salaries is:

$38,500 \leq x \leq 41,100$

This inequality represents the range of possible salaries, which is between $\$38,500$ and $\$41,100$ . By using this inequality, we can determine whether a salary, $x$ , falls within the range of possible salaries.

Key Takeaways

The average starting salary for an editor at a textbook company is $\$39,800$ .
The actual salaries can vary by less than $\$1,300$ .
The correct inequality to determine whether a salary, $x$ , falls within the range of possible salaries is $38,500 \leq x \leq 41,100$ .

As a prospective editor at a textbook company, you may have questions about the average salary and the range of possible salaries. Here are some frequently asked questions and answers to help you better understand the situation.

Q: What is the average starting salary for an editor at a textbook company?

A: The average starting salary for an editor at a textbook company is $\$39,800$ .

Q: How much can the actual salaries vary?

A: The actual salaries can vary by less than $\$1,300$ . This means that the lowest possible salary is $\$39,800 - \$1,300 = \$38,500$ , and the highest possible salary is $\$39,800 + \$1,300 = \$41,100$ .

Q: What is the correct inequality to determine whether a salary, $x$ , falls within the range of possible salaries?

A: The correct inequality to determine whether a salary, $x$ , falls within the range of possible salaries is:

$38,500 \leq x \leq 41,100$

Q: How do I use the inequality to determine whether a salary, $x$ , falls within the range of possible salaries?

A: To use the inequality, you need to check whether the salary, $x$ , satisfies both the lower and upper bounds. If the salary, $x$ , is greater than or equal to $\$38,500$ and less than or equal to $\$41,100$ , then it falls within the range of possible salaries.

Q: What if I want to determine whether a salary of $\$40,000$ falls within the range of possible salaries?

A: To determine whether a salary of $\$40,000$ falls within the range of possible salaries, you need to check whether it satisfies both the lower and upper bounds. Since $\$40,000$ is greater than $\$38,500$ and less than $\$41,100$ , it falls within the range of possible salaries.

Q: Can I use the inequality to determine whether a salary, $x$ , is higher or lower than the average salary?

A: Yes, you can use the inequality to determine whether a salary, $x$ , is higher or lower than the average salary. If the salary, $x$ , is greater than $\$39,800$ , then it is higher than the average salary. If the salary, $x$ , is less than $\$39,800$ , then it is lower than the average salary.

Q: What if I want to determine whether a salary of $\$42,000$ falls within the range of possible salaries?

A: To determine whether a salary of $\$42,000$ falls within the range of possible salaries, you need to check whether it satisfies both the lower and upper bounds. Since $\$42,000$ is greater than $\$41,100$ , it does not fall within the range of possible salaries.

Q: Can I use the inequality to determine whether a salary, $x$ , is within a certain range of the average salary?

A: Yes, you can use the inequality to determine whether a salary, $x$ , is within a certain range of the average salary. For example, if you want to determine whether a salary, $x$ , is within $\$1,000$ of the average salary, you can use the inequality:

$38,800 \leq x \leq 40,800$

Conclusion

In conclusion, the correct inequality to determine whether a salary, $x$ , falls within the range of possible salaries is:

$38,500 \leq x \leq 41,100$

By using this inequality, you can determine whether a salary, $x$ , falls within the range of possible salaries and make informed decisions about your career choices and salary expectations.

Key Takeaways

The average starting salary for an editor at a textbook company is $\$39,800$ .
The actual salaries can vary by less than $\$1,300$ .
The correct inequality to determine whether a salary, $x$ , falls within the range of possible salaries is $38,500 \leq x \leq 41,100$ .
You can use the inequality to determine whether a salary, $x$ , is higher or lower than the average salary.
You can use the inequality to determine whether a salary, $x$ , is within a certain range of the average salary.