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 4/5 n − 12 > 24

Question

, where n equals the number, to help solve this problem. Solve her inequality.(1 point)
Responses

n>15
n greater than 15

n>28.8
n greater than 28.8

n>9.6
n greater than 9.6

n>45

Answer 1

To solve Lucia's inequality \( \frac{4}{5} n - 12 > 24 \), we will first add 12 to both sides of the inequality:

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

This simplifies to:

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

Next, we will multiply both sides of the inequality by \( \frac{5}{4} \) to solve for \( n \):

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

Calculating the right side:

\[ n > 36 \times \frac{5}{4} = 36 \times 1.25 = 45 \]

Therefore, the solution to Lucia's inequality is:

\[ n > 45 \]

So the correct response is:

n > 45