Solve for $x$: $$ \frac{1}{2} - \frac{1}{3} = \frac{1}{x}.$$
Subtract 1/3 from 1/2 by finding a common denominator: \[
\frac{1}{2}-\frac{1}{3}=\frac{3}{6}-\frac{2}{6}=\frac{1}{6}.
\] Solving $\frac{1}{6}=\frac{1}{x}$ we find $x=\boxed{6}$.
6
Level 1
Algebra
Problem: Solve for $x$: $$ \frac{1}{2} - \frac{1}{3} = \frac{1}{x}.$$
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To solve for $x$, first simplify the left side of the equation. Find a common denominator for the fractions $\frac{1}{2}$ and $\frac{1}{3}$. The least common multiple of 2 and 3 is 6. Rewrite the fractions: 

$$ \frac{1}{2} = \frac{3}{6} $$
$$ \frac{1}{3} = \frac{2}{6} $$

Now substitute these values back into the equation:

$$ \frac{3}{6} - \frac{2}{6} = \frac{1}{x} $$

Perform the subtraction on the left side:

$$ \frac{3 - 2}{6} = \frac{1}{6} $$

This simplifies to:

$$ \frac{1}{6} = \frac{1}{x} $$

Next, to find $x$, take the reciprocal of both sides of the equation:

$$ x = 6 $$

Thus, the solution to the equation is $6$.<|END_OF_LATENT|> The final answer is $6$.