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).