Question

type the correct answer in the box. use numerals instead of words. what is the solution to this equation? 3(n - 9) - 2(n + 4) = 6n n = \boxed{}

Explanation:

Step1: Expand the brackets

First, we expand the left - hand side of the equation using the distributive property \(a(b + c)=ab+ac\) and \(a(b - c)=ab - ac\).
For \(3(n - 9)\), we get \(3\times n-3\times9 = 3n-27\).
For \(-2(n + 4)\), we get \(-2\times n+(-2)\times4=-2n - 8\).
So the left - hand side of the equation becomes \((3n-27)+(-2n - 8)\).
Combining like terms: \(3n-2n-27 - 8=n-35\).
The equation is now \(n - 35=6n\).

Step2: Solve for n

Subtract \(n\) from both sides of the equation:
\(n - n-35=6n - n\)
\(-35 = 5n\)

Then divide both sides by 5:
\(n=\frac{-35}{5}=-7\)

Answer:

\(-7\)