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>15
n greater than 15

n>45
n greater than 45

n>28.8
n greater than 28.8

n>9.6

Answer 1

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

1. Add 12 to both sides: \[ \frac{4}{5}n - 12 + 12 > 24 + 12 \] This simplifies to: \[ \frac{4}{5}n > 36 \]

2. Multiply both sides by \( \frac{5}{4} \) to isolate \( n \): \[ n > 36 \cdot \frac{5}{4} \]

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

So the solution to the inequality is: \[ n > 45 \]

Thus, the correct response is:

• n > 45