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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.

Respuesta :

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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:

[tex]|m-32|\leq 8[/tex]

Range: [tex]24\leq m\leq 40[/tex]

Step-by-step 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.

[tex]|\text{Actual}-\text{Ideal}|\leq \text{tolerance}[/tex]

[tex]|m-32|\leq 8[/tex]

Using absolute value inequality definition, if [tex]|u|\leq a[/tex], then [tex]-a\leq u\leq a[/tex], we will get:

[tex]-8\leq m-32\leq 8[/tex]

[tex]-8+32\leq m-32+32\leq 8+32[/tex]

[tex]24\leq m\leq 40[/tex]

Therefore, the range of medication costs at the pharmacy is [tex]24\leq m\leq 40[/tex].

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