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Twelve less than four-fifths of a number is more than 24. What are all the possible values of the number? Lucia wrote the inequality 4/5n−12>24
, where n equals the number, to help solve this problem. Solve her inequality.(1 point)
Responses

n>45
n greater than 45

n>9.6
n greater than 9.6

n>28.8
n greater than 28.8

n>15
n greater than 15

1 answer

To solve the inequality \( \frac{4}{5}n - 12 > 24 \), we will first isolate \( n \).

  1. Start by adding 12 to both sides of the inequality:

    \[ \frac{4}{5}n > 24 + 12 \]

    \[ \frac{4}{5}n > 36 \]

  2. Next, to eliminate the fraction, multiply both sides by \( \frac{5}{4} \):

    \[ n > 36 \times \frac{5}{4} \]

    \[ n > 36 \times 1.25 \]

    \[ n > 45 \]

Thus, the solution to the inequality is:

\[ n > 45 \]

So, the correct response is: n > 45.