Answer
$x=-2{\sqrt 2}$
Work Step by Step
Given: $\frac{4}{3}cos^{-1}\frac{x}{4}=\pi$
$\frac{4}{3}cos^{-1}\frac{x}{4}=\frac{3 \pi}{4}$
$\frac{x}{4}=cos(\frac{3 \pi}{4})$
$x=4cos(\frac{3 \pi}{4})$ (Multiply by 4)
Apply definition of arccosine.
$x=-4(\frac{\sqrt 2}{2})$
Hence, $x=-2{\sqrt 2}$
