To solve this problem, we need to use the concept of inverse proportionality. When two quantities are inversely proportional to each other, their product is always a constant. Mathematically, if [tex]\(x\)[/tex] is inversely proportional to [tex]\(y\)[/tex], then [tex]\(x \cdot y = k\)[/tex], where [tex]\(k\)[/tex] is a constant.
Given the problem:
- [tex]\( x = 60 \)[/tex] when [tex]\( y = 0.5 \)[/tex].
Let's first find the constant [tex]\( k \)[/tex]:
[tex]\[ k = x \cdot y = 60 \cdot 0.5 = 30 \][/tex]
Now, we need to find [tex]\( x \)[/tex] when [tex]\( y = 12 \)[/tex]. According to the inverse proportionality:
[tex]\[ x \cdot y = k \][/tex]
Substituting the known values:
[tex]\[ x \cdot 12 = 30 \][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{30}{12} \][/tex]
[tex]\[ x = 2.5 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 12 \)[/tex] is:
[tex]\[ \boxed{2.5} \][/tex]
