Question

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

|x − 37,500| ≤ 4,500
|x − 4,500| ≤ 37,500
|x − 37,500| ≥ 4,500
|x − 4,500| ≥ 37,500

Answer 1

|x − 37,500| ≤ 4,500

Explanation:

Let x represents the new salary paid (In dollars ),

∵ The actual salary = $ 37,500

∵ Maximum difference in salaries = $ 4500

Case 1 : If x > 0

⇒ x - 37500 ≤ 4500 -----(1)

Case 2 : If x < 0

⇒ 37500 - x ≤ 4500

⇒ -(x-37500) ≤ 4500 -----(2)

By combining inequalities (1) and (2),

| x - 37500 | ≤ 4500 ( ∵ |a| < b ⇒ -a < b or a < b )

Which is the absolute value inequality to determine the range of salaries at this company.

FIRST option is correct.

Answer 2

|x − 37,500| ≤ 4,500

Explanation:

salary - 37,500 can be up +4500 or as negative -4500

as much as means less than or equal to

We use absolute values to indicate this

|x − 37,500| ≤ 4,500