#### Answer

$x=-\dfrac{1}{3}$

#### Work Step by Step

$\dfrac{1}{x}=\dfrac{4}{3x}+1$
Let's multiply the whole equation by $3x$, which is the least common multiple of the denominators present in the equation.
We'll do this to avoid working with fractions.
$(3x)(\dfrac{1}{x}=\dfrac{4}{3x}+1)$
$(3x)(\dfrac{1}{x})=(3x)(\dfrac{4}{3x})+3x$
Simplify:
$3=4+3x$
Solve for $x$:
$3x=3-4$
$3x=-1$
$x=-\dfrac{1}{3}$