Final answer:
There is no value for n that makes the equation 2/3n+2 = -2/3(n-9) true. Upon solving, the resulting statement is 2 = 6, which is not possible, indicating no solution exists.
Step-by-step explanation:
The question involves solving a simple linear equation to find the value of the variable n that makes the equation true. The equation given is 2/3n+2 = -2/3(n-9). To solve for n, we first distribute the -2/3 across the (n-9), and then we move all terms containing n to one side and the constants to the other.
First step is to distribute -2/3:
(2/3)n + 2 = (-2/3)n + 6
Next, we get all n terms on one side by adding (2/3)n to both sides:
2 = 6
This implies that there is no value for n that would make the original equation true, because when n terms are eliminated, the equation simplifies to 2 = 6, which is not a true statement and indicates that there is no solution to the equation.