Question

A pharmacy claims that the average medication costs $32 but it could differ as much as $8. Write and solve an absolute value inequality to determine the range of medication costs at this pharmacy.

Answer 1

A) |x − 32| ≥ 8; The medication costs range from $24 to $40
B)|x − 32| ≥ 8; The medications cost less than $24 or greater than $40.
C) |x − 32| ≤ 8; The medication costs range from $24 to $40
D) |x − 32| ≤8; The medications cost less than $24 or greater than $40.

So,

We can tell that the most expensive medication costs $40 and the cheapest costs $24. Thus, only options A and C are left.

To see which inequality is true, test a value, such as $30, in the equation in option C.

|30 - 32| ≤ 8
|-2| ≤ 8
2 ≤ 8

Option C is correct.

Answer 2

`|m-32|\leq 8`

Range:
`24\leq m\leq 40`

Explanation:

Let m represent cost of medication.

We have been given that a pharmacy claims that the average medication costs $32 but it could differ as much as $8.

`|\text{Actual}-\text{Ideal}|\leq \text{tolerance}`

`|m-32|\leq 8`

Using absolute value inequality definition, if
`|u|\leq a`, then
`-a\leq u\leq a`, we will get:

`-8\leq m-32\leq 8`

`-8+32\leq m-32+32\leq 8+32`

`24\leq m\leq 40`

Therefore, the range of medication costs at the pharmacy is
`24\leq m\leq 40`.