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 d

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.

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Margaret 16 mins 2021-10-13T06:29:04+00:00 2 Answers 0

Answers ( )

    0
    2021-10-13T06:30:47+00:00

    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.

    0
    2021-10-13T06:30:58+00:00

    Answer:

    |m-32|\leq 8

    Range: 24\leq m\leq 40

    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.

    |\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.

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