Question

A publisher claims that the average salary paid at its company is $37,500 but it could differ as much as $4,500. Write and solve an absolute value inequality to determine the range of salaries at this company. (2 points)

Answer 1

The range of salaries at this company is from $33,000 to $42,000.

Explanation:

The absolute value inequality equation |x-$37,500| < $4,500 means that the differences in salary from the average ($37,500) have to be equal or less than $4,500. Solving the absolute value inequality equation where x is the salary:

|x-$37,500| < $4,500

-$4,500 < x - $37,500 < $4,500

-$4,500 + $37,500 < x - $37,500 + $37,500 < $4,500 + $37,500

$33,000 < x < $42,000

If x is the salary, it means that an employee salary can be from $33,000 to $42,000.

Answer 2

average salary is equal to 37,500

maximum salary is 4500 +37,500 = 42,000

mnimum salary is 37,500 - 4500 = 33,000

the equation is |x − 37500| ≤ 4500 meaning the salaries range from $33,000 to $42,000