If x is inversely proportional to y, and y = 7 when x = 16, find the value of x, when y = 2.

The correct answer is 56.

Step 1: Understand the relationship between x and y.
When two variables $x$ and $y$ are inversely proportional, their product is equal to a constant, $k$.
This inverse variation relationship can be written as:

$x·y=k$

or equivalently:

$x_1{y}_1=x_2{y}_2$

Step 2: Find the constant of proportionality (k).
We are given that $y=7$ when $x=16$.
Substitute these values into the formula to find $k$:

$k=16·7$

$k=112$

Step 3: Calculate the value of x when y = 2.
Now, we use the constant $k=112$ and the given value $y=2$ to find the new value of $x$:

$x·2=112$

Divide both sides by 2:

$x=\frac{112}{2}$

$x=56$

Thus, when $y=2$, the value of $x$ is 56.