Answer
$c= 16/3, -6$
Work Step by Step
$abs (3c+1) -4 =13$
$abs (3c+1) -4+4 =13+4$
$abs(3c+1) = 17$
$3c+1 = 17$ and $3c+1=-17$
$3c+1=17$
$3c = 16$
$3c/3= 16/3$
$c=16/3$
$3c+1=-17$
$3c+1-1=-17-1$
$3c = -18$
$3c/3=-18/3$
$c=-6$
Let $c=16/3$:
$abs(3c+1)-4=13$
$abs(3*16/3+1)-4=13$
$abs(16+1)-4=13$
$abs(17)-4=13$
$17-4 = 13$ is a true statement
Let $c=-6$:
$abs(3c+1)-4=13$
$abs(3*-6+1)-4=13$
$abs(-18+1)-4=13$
$abs(-17)-4=13$
$17-4=13$ is a true statement
