Sure, let's solve the equation step by step.
The given equation is:
[tex]\[
\frac{-n-1}{4} = -8
\][/tex]
1. Isolate the numerator:
To eliminate the fraction, multiply both sides of the equation by 4:
[tex]\[
4 \cdot \frac{-n-1}{4} = 4 \cdot -8
\][/tex]
Simplifying this, we get:
[tex]\[
-n - 1 = -32
\][/tex]
2. Solve for [tex]\( n \)[/tex]:
Next, we need to get [tex]\( n \)[/tex] by itself. Start by adding 1 to both sides of the equation:
[tex]\[
-n - 1 + 1 = -32 + 1
\][/tex]
Simplifying the left side and the right side, we get:
[tex]\[
-n = -31
\][/tex]
3. Get [tex]\( n \)[/tex] by itself:
Finally, we need [tex]\( n \)[/tex] to be positive. To do this, multiply both sides by -1:
[tex]\[
-1 \cdot -n = -1 \cdot -31
\][/tex]
Simplifying this, we get:
[tex]\[
n = 31
\][/tex]
So, the solution to the equation is:
[tex]\[
n = 31
\][/tex]
