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)

Answer 1

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

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

2. Multiply both sides by \( \frac{5}{4} \) to isolate \( n \) (note that we multiply by a positive number, which does not change the direction of the inequality): \[ n > 36 \cdot \frac{5}{4} \]

   Calculate \( 36 \cdot \frac{5}{4} \): \[ 36 \cdot \frac{5}{4} = \frac{180}{4} = 45 \]

3. Therefore, we find: \[ n > 45 \]

The solution to Lucia's inequality is that the number \( n \) must be greater than 45. Thus, the possible values for the number are all values greater than 45.