#### Answer

$x=15$
$x=-13$

#### Work Step by Step

To solve an absolute value equation, we solve for $x$ using the positive and negative value of the non-absolute value side (after isolating the absolute value expression).
First, we isolate the absolute value expression by subtracting 19 from both sides, giving us $|x-1|=14$.
Now, we solve $x-1=14$ and $x-1=-14$.
To solve $x-1=14$, we add 1 to both sides to isolate $x$, giving us $x=15$.
To solve $x-1=-14$, we add 1 to both sides to isolate $x$, giving us $x=-13$.