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.

|x − 32| ≥ 8; The medication costs range from $24 to $40

|x − 32| ≥ 8; The medications cost less than $24 or greater than $40.

|x − 32| ≤ 8; The medication costs range from $24 to $40

|x − 32| ≤8; The medications cost less than $24 or greater than $40.

Answer 1

the answer is C the third one

Answer 2

It looks like you're supposed to pick a combination of two answers:
an absolute-value inequality, and
a sentence describing the meaning of that inequality.

We've got two choices for each, and therefore four possible combinations of choices.

First, let's tackle the sentence description. We're told that
"it [the cost] could differ [from the average of $32] as much as $8."
That sets a maximum value for the difference; it's UP TO $8.
If the cost is less than average, it could be as little as
$32 - $8 = $24
and if the cost is more than average, it could be as much as
$32 + $8 = $40.
So the medication costs range from $24 to $40, and we want an answer that states that.

Now for the inequalities:
|x - 32| describes the SIZE of the difference. Using the absolute-value function means we don't distinguish between
x - 32
and
32 - x
as far as our interests are concerned; we eliminate the sign from the subtraction and just look at the size of the difference.

But in the case we're looking at, we've got a MAXIMUM value for the difference; it can't be more than 8. The inequality
|x - 32| ≥ 8
says the difference is 8 or MORE, so we don't want that. Instead, we want
|x - 32| ≤ 8
which says the difference is anywhere from 0 to 8.

Combining these conclusions, we see we're looking for this answer:
|x - 32| ≤ 8; The medication costs range from $24 to $40
which is the third one listed.