Answer
The given equation has no solutions.
Work Step by Step
We have to solve the equation as follows:
$\cos x-5=3\cos x+6$
Arrange the given equation in such a way that the cosine functions are on one side and the real numbers are on the other as follows:
$\begin{align}
& \cos x-3\cos x=6+5 \\
& -2\cos x=11 \\
& \cos x=\frac{-11}{2}
\end{align}$
Thus, the cosine value of all the numbers always lies in the interval $\left[ -1,1 \right]$; the cosine value cannot be less than 1. So, $\cos x=\frac{-11}{2}$ is not possible.
