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>28.8
n greater than 28.8

n>15
n greater than 15

n>9.6
n greater than 9.6

n>45

choose one above

Answer 1

To solve the inequality \( \frac{4}{5}n - 12 > 24 \):

1. Start by isolating the term with \( n \): \[ \frac{4}{5}n - 12 > 24 \] Add 12 to both sides: \[ \frac{4}{5}n > 24 + 12 \] \[ \frac{4}{5}n > 36 \]

2. Next, multiply both sides by \( \frac{5}{4} \) to solve for \( n \): \[ n > 36 \cdot \frac{5}{4} \] Calculate \( 36 \cdot \frac{5}{4} \): \[ 36 \cdot \frac{5}{4} = 36 \cdot 1.25 = 45 \]

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

Therefore, the correct response from your choices is:

• n > 45