Answer
$x\in(-1,3)$
Work Step by Step
The square root function is defined for nonnegative real numbers, and is an increasing function.
This means that if a and b are nonnegative,
$a \lt b\Rightarrow\sqrt{a} \lt \sqrt{b}$
An alternate definition of the absolute value is $|x|=\sqrt{x^{2}}$.
Both sides of the inequality sign are nonnegative, so we may take the square root of both sides, with the direction of inequality being unchanged:
$\sqrt{(x-1)^{2}} \lt \sqrt{4}$
$|x-1| \lt 2$
By property 6 from the table 'Absolute Values and Intervals", it follows that
$-2 \lt x-1 \lt 2$
Add 1 to each side
$-1 \lt x \lt 3$
This solution set in interval form is
$x\in(-1,3)$
