What number should be subtracted from $-2$ to get $\dfrac{7}{11}$?

Let the required number be $x$.

According to the given condition,

$\Rightarrow -2 - x = \dfrac{7}{11} \\[1em] \Rightarrow x = -2 - \dfrac{7}{11} \\[1em] \Rightarrow x = \dfrac{(-2) \times 11 - 7}{11} \\[1em] \Rightarrow x = \dfrac{-22 - 7}{11} \\[1em] \Rightarrow x = \dfrac{-29}{11} = -2\dfrac{7}{11}$

Hence, the required number is $\mathbf{\dfrac{-29}{11}}$.