Question

select the correct answer
the average starting salary for an editor at a textbook company is $39,800. the actual salaries can vary by less than $1,300. which inequality can be used to determine whether a salary, x, falls within this range? what is the range of starting salaries at the company?
a. |x - 39,800| < 1,300
the range of salaries is from $38,500 to $41,100.
b. |x + 1,300| ≥ 39,800
the range of salaries is from $39,800 to $41,100.
c. |1,300 - x| < 39,800
the range of salaries is from $38,500 to $39,800.
d. |x + 39,800| < 1,300
the range of salaries is from $38,500 to $41,100.

Explanation:

Step1: Identify absolute value inequality

The difference between actual salary $x$ and average salary $39800$ is less than $1300$, so the inequality is $|x - 39800| < 1300$.

Step2: Solve the absolute value inequality

Rewrite the inequality as a compound inequality:
$$-1300 < x - 39800 < 1300$$
Add $39800$ to all parts:
$$39800 - 1300 < x < 39800 + 1300$$
$$38500 < x < 41100$$

Answer:

A. $|x - 39,800| < 1,300$
The range of salaries is from $38,500 to $41,100.