Answer
$x = \frac{d+1}{1-c}$
Work Step by Step
$x - 1 = cx + d$
$x - 1 + 1 = cx + d + 1$
$x = cx + d + 1$
$x - cx = cx +d + 1 - cx$
$x- cx = d + 1$
$x(1 - c) = d+ 1$
$x(1 - c) \times \frac{1}{1-c} = (d+ 1)\times\frac{1}{1-c}$
$x = \frac{d+1}{1-c}$