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 45n−12>24, where n equals the number, to help solve this problem. Solve her inequality.(1 point)
A: n>9.6
B: n>15
C: n>45
D: n>28.8
D: n>28.8
To solve the inequality, we have 45n - 12 > 24.
First, let's isolate the variable n. We'll start by adding 12 to both sides of the inequality:
45n - 12 + 12 > 24 + 12
This simplifies to:
45n > 36
Next, we want to isolate n by dividing both sides of the inequality by 45:
(45n)/45 > 36/45
This simplifies to:
n > 36/45
Now, let's simplify the fraction:
n > 4/5
The fraction 36/45 can be reduced to 4/5.
Therefore, the solution to the inequality is n > 4/5.
To find the possible values of n, we need to convert 4/5 to a decimal.
4 divided by 5 equals 0.8.
So, the possible values of the number (n) are all numbers greater than 0.8.
Among the given options, the only one that represents numbers greater than 0.8 is:
A: n > 9.6
Therefore, the correct answer is A: n > 9.6.
To solve the inequality 45n - 12 > 24, we can go through the following steps:
1. Add 12 to both sides of the inequality:
45n - 12 + 12 > 24 + 12
45n > 36
2. Divide both sides of the inequality by 45:
(45n)/45 > 36/45
n > 36/45
n > 0.8
Therefore, the correct answer is A: n > 0.8.
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, where n equals the number, to help solve this problem. Solve her inequality.(1 point)
A: n>9.6
B: n>15
C: n>45
D: n>28.8