Final answer:
To solve the given equation, distribute and simplify, get rid of denominators, combine like terms, and isolate the variable. Divide both sides of the equation to find the value of n.
Step-by-step explanation:
To solve the equation 1/2(-4+6n) = 1/3n 2/3(n+9), we can start by simplifying both sides of the equation. First, distribute the 1/2 on the left side and distribute the 2/3 on the right side:
-2 + 3n = 2n/3 + 6
Next, get rid of the denominators by multiplying both sides of the equation by the least common denominator, which in this case is 6:
-12 + 18n = 4n + 36
Now, combine like terms and isolate the variable:
18n - 4n = 36 + 12
14n = 48
Finally, divide both sides of the equation by 14 to solve for n:
n = 48/14
n = 24/7