Define the relationship

Since x is inversely proportional to y, their product is a constant k, expressed as $x \times y = k$.

$x \times y = k$

Calculate the constant k

Using the given values $x = 7$ and $y = 6$, we find the constant $k = 7 \times 6 = 42$.

$k = 7 \times 6 = 42$

Solve for x

Now set the product to 42 for $y = 64$: $x \times 64 = 42$. Solving for x gives $x = 42/64$.

$x = \frac{42}{64}$

Simplify the fraction

Simplify the fraction by dividing both numerator and denominator by 2: $x = 21/32$.

$x = \frac{21}{32}$