Let's solve the equation to find the correct value of [tex]\( n \)[/tex].
The given equation is:
[tex]\[ 6n - 2(4n + 7) + 4 = -2 \][/tex]
First, we need to distribute the [tex]\(-2\)[/tex] inside the parentheses:
[tex]\[ 6n - 2 \cdot 4n - 2 \cdot 7 + 4 = -2 \][/tex]
[tex]\[ 6n - 8n - 14 + 4 = -2 \][/tex]
Next, combine like terms:
Starting with the [tex]\( n \)[/tex] terms:
[tex]\[ 6n - 8n = -2n \][/tex]
Then combining the constant terms:
[tex]\[ -14 + 4 = -10 \][/tex]
So the equation simplifies to:
[tex]\[ -2n - 10 = -2 \][/tex]
Next, isolate the [tex]\( n \)[/tex] term by adding 10 to both sides of the equation:
[tex]\[ -2n - 10 + 10 = -2 + 10 \][/tex]
[tex]\[ -2n = 8 \][/tex]
Finally, solve for [tex]\( n \)[/tex] by dividing both sides by [tex]\(-2\)[/tex]:
[tex]\[ n = \frac{8}{-2} \][/tex]
[tex]\[ n = -4 \][/tex]
Therefore, the value of [tex]\( n \)[/tex] that makes the equation true is:
[tex]\[ \boxed{-4} \][/tex]
