## Precalculus (6th Edition) Blitzer

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.