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 $x=-13$.