Answer
$\dfrac{dx}{dt} = 3$
Work Step by Step
Given: $\dfrac{dy}{dt}=-2$ and $2x+3y=12$
Thus,on differentiating $y$ with respect to time, we get
$\dfrac{d(2x+3y)}{dt}$ = $\frac{d (12)}{dt}$
or, $2\dfrac{dx}{dt} + 3\dfrac{dy}{dt}=0$
or, $2\dfrac{dx}{dt} = (-3)(-2)$
Thus, the answer is :$\dfrac{dx}{dt} = 3$
