first solve for x
[tex]\begin{gathered} x+1>-\frac{6}{3} \\ \\ x+1>-2 \\ x>-2-1 \\ x>-3 \end{gathered}[/tex]This tells us that the values that x can take must be greater than -3
so the interval notation is
[tex](-3,\infty)[/tex]because these numbers are greater than -3 not including it