To solve for the value of [tex]\( n \)[/tex] that makes the equations [tex]\( 4(0.5n - 3) \)[/tex] and [tex]\( n - 0.25(12 - 8n) \)[/tex] equal to each other, let's follow these steps:
1. Write down the equations:
[tex]\[
4(0.5n - 3) \quad \text{and} \quad n - 0.25(12 - 8n)
\][/tex]
2. Simplify each expression:
For the first expression:
[tex]\[
4(0.5n - 3) = 4 \cdot 0.5n - 4 \cdot 3 = 2n - 12
\][/tex]
For the second expression:
[tex]\[
n - 0.25(12 - 8n) = n - 0.25 \cdot 12 + 0.25 \cdot 8n = n - 3 + 2n = 3n - 3
\][/tex]
3. Set the simplified expressions equal to each other:
[tex]\[
2n - 12 = 3n - 3
\][/tex]
4. Solve for [tex]\( n \)[/tex]:
First, subtract [tex]\( 2n \)[/tex] from both sides:
[tex]\[
-12 = n - 3
\][/tex]
Next, add 3 to both sides:
[tex]\[
-12 + 3 = n
\][/tex]
Simplifying the left-hand side:
[tex]\[
-9 = n
\][/tex]
So, the value of [tex]\( n \)[/tex] that makes the two equations equal is [tex]\( n = -9 \)[/tex].
Thus, the answer is:
[tex]\[
\boxed{-9}
\][/tex]
