解:解方程$3(2x - 1) = k + 2x$
$6x - 3 = k + 2x$
$6x - 2x = k + 3$
$4x = k + 3$
$x = \frac{k + 3}{4}$
解方程$8 - k = 2(x + 1)$
$8 - k = 2x + 2$
$-2x = 2 - 8 + k$
$-2x = k - 6$
$x = \frac{6 - k}{2}$
因?yàn)閮煞匠痰慕饣橄喾磾?shù),所以$\frac{k + 3}{4} + \frac{6 - k}{2} = 0$
$\frac{k + 3}{4} + \frac{12 - 2k}{4} = 0$
$\frac{k + 3 + 12 - 2k}{4} = 0$
$-k + 15 = 0$
$k = 15$
答:$k$的值為$15$。