P = 6n + 18 P = 6 n + 18 P = 9n + 6 P = 9 n + 6 P = 6n + 9 P = 6 n + 9 P = 9n + 12

Answer 1

Since we are given multiple equations, we need to solve for the variable n by setting the equations equal to each other.

So setting the first equation equal to the second equation:
6n + 18 = 6n + 18
This equation is true for all values of n, so there are infinite solutions.

Now setting the second equation equal to the third equation:
6n + 18 = 9n + 6
Subtracting 6n from both sides:
18 = 3n + 6
Subtracting 6 from both sides:
12 = 3n
Dividing both sides by 3:
n = 4

Setting the third equation equal to the fourth equation:
9n + 6 = 9n + 6
This equation is true for all values of n, so there are infinite solutions.

Setting the fourth equation equal to the fifth equation:
9n + 6 = 6n + 9
Subtracting 6 from both sides:
9n = 6n + 3
Subtracting 6n from both sides:
3n = 3
Dividing both sides by 3:
n = 1

Setting the fifth equation equal to the sixth equation:
6n + 9 = 6n + 9
This equation is true for all values of n, so there are infinite solutions.

Setting the sixth equation equal to the seventh equation:
6n + 9 = 9n + 12
Subtracting 6n from both sides:
9 = 3n + 12
Subtracting 12 from both sides:
-3 = 3n
Dividing both sides by 3:
n = -1

Therefore, there are three distinct solutions for the variable n: n = 4, n = 1, and n = -1.