Question

the average starting salary for an editor at a textbook com can be used to determine whether a salary, x, falls within
a. (|x + 1,300| geq 39,800)
the range of salaries is from $39,800 to $4
b. (|x + 39,800| < 1,300)
the range of salaries is from $38,500 to $4
c. (|1,300 - x| < 39,800)
the range of salaries is from $38,500 to $39
d. (|x - 39,800| < 1,300)
the range of salaries is from $38,500 to $4

Explanation:

Step1: Recall absolute value inequality rules

For $|x - a| < b$, it means $a - b < x < a + b$, where $a$ is the midpoint (average) and $b$ is the deviation from the midpoint.

Step2: Identify midpoint and deviation

The average salary is $39,800$, so $a = 39800$. The range is $38500$ to $41100$. Calculate deviation: $39800 - 38500 = 1300$, so $b = 1300$.

Step3: Match to correct inequality

The inequality for salary $x$ within this range is $|x - 39800| < 1300$, which matches option D.

Answer:

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