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

Question

, 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>15
n greater than 15

n>28.8

Answer 1

To solve the inequality that Lucia wrote, \( \frac{4}{5}n - 12 > 24 \), we can follow these steps:

1. Add 12 to both sides of the inequality: \[ \frac{4}{5}n > 24 + 12 \] \[ \frac{4}{5}n > 36 \]

2. Multiply both sides by \( \frac{5}{4} \) to isolate \( n \) (remembering to keep the inequality the same since we are multiplying by a positive number): \[ n > 36 \cdot \frac{5}{4} \]

3. Calculate \( 36 \cdot \frac{5}{4} \): \[ 36 \cdot \frac{5}{4} = 36 \cdot 1.25 = 45 \]

Thus, the solution to the inequality \( n > 45 \).

The correct response is:

n>45 (n greater than 45).