Inverse z transform using partial fraction
Since the Z-transform is linear, you can just use a Transform table to find the discrete time equivalent of
$$ X(z) = \frac{-7/3}{z-1} + \frac{22/3}{z-4}.$$
Look separetly for an inverse of,
$$\frac{-7/3}{z-1} = A(z), $$ and 
$$ \frac{22/3}{z-4} = B(z).$$
Then add the two inverses to get the discrete time \$x[k] = a[k] + b[k]\$.