Let's solve the equation step-by-step to find which value of [tex]\( n \)[/tex] makes the equation true.
The equation given is:
[tex]\[ 6n - 2(4n + 7) + 4 = -2 \][/tex]
First, let's 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:
[tex]\[ (6n - 8n) + (-14 + 4) = -2 \][/tex]
[tex]\[ -2n - 10 = -2 \][/tex]
To isolate [tex]\( n \)[/tex], add 10 to both sides:
[tex]\[ -2n - 10 + 10 = -2 + 10 \][/tex]
[tex]\[ -2n = 8 \][/tex]
Now, divide both sides by [tex]\(-2\)[/tex]:
[tex]\[ n = \frac{8}{-2} \][/tex]
[tex]\[ n = -4 \][/tex]
The value of [tex]\( n \)[/tex] that makes the equation true is:
[tex]\[ n = -4 \][/tex]
Therefore, the correct answer is [tex]\(\boxed{-4}\)[/tex].
