If x is a negative integer, find the solution set of $\dfrac{2}{3}+\dfrac{1}{3} (x + 1) \gt 0$.

Given,

$\dfrac{2}{3}+\dfrac{1}{3} (x + 1) \gt 0 \\[0.5em] \Rightarrow \dfrac{2}{3} +\dfrac{x}{3} + \dfrac{1}{3} \gt 0 \\[0.5em] \Rightarrow \dfrac{x}{3} + 1 \gt 0 \\[0.5em] \Rightarrow \dfrac{x}{3} \gt – 1 \\[0.5em] \Rightarrow x \gt -3$

x is a negative integer Solution set = {-2, –1}.