To determine the value of [tex]\( x \)[/tex] for the inverse variation equation [tex]\( x \cdot y = k \)[/tex] when given specific values for [tex]\( y \)[/tex] and [tex]\( k \)[/tex], we can proceed through the following steps:
1. Identify the given values:
We know that [tex]\( y = 4 \)[/tex] and [tex]\( k = 7 \)[/tex].
2. Set up the inverse variation equation:
The equation for inverse variation is
[tex]\[
x \cdot y = k
\][/tex]
3. Substitute the known values into the equation:
Plug in [tex]\( y = 4 \)[/tex] and [tex]\( k = 7 \)[/tex] into the equation:
[tex]\[
x \cdot 4 = 7
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
To isolate [tex]\( x \)[/tex], divide both sides of the equation by 4:
[tex]\[
x = \frac{7}{4}
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 4 \)[/tex] and [tex]\( k = 7 \)[/tex] is [tex]\( \frac{7}{4} \)[/tex].
So, the correct answer is:
[tex]\(\boxed{\frac{7}{4}}\)[/tex]
