Answer
$x=\frac{7\pi}{6}+2n\pi$ and $x=\frac{11\pi}{6}+2n\pi$, where $n$ is an integer.
Work Step by Step
$3~sin~x+1=sin~x$
$2~sin~x=-1$
$sin~x=-\frac{1}{2}$
The period of $sin~x$ is $2\pi$. The solutions in the interval: $[0,2\pi)$ are:
$x=\frac{7\pi}{6}$ and $x=\frac{11\pi}{6}$
Now, add multiples of $2\pi$ to each of the solutions:
$x=\frac{7\pi}{6}+2n\pi$ and $x=\frac{11\pi}{6}+2n\pi$, where $n$ is an integer.
