Question regarding an inequality in Spivak's Calculus

Question

On page 92 in the 4th Edition of Spivak's Calculus, he mentions an inequality while discussing Limits.

|x-3| < 1, or 2 < x < 4

I understand how he got the upper (or < 4) portion of the inequality, but how was the number "2" determined. I might be missing a subtle point here regarding absolute values so I thought I'd ask. Appreciate it in advanced!

Answer 1

$$|x-3| < 1$$ is equivalent to $$-1 < x-3 < 1.$$ It may be helpful to read "$|x-3|$" as "the distance between $x$ and $3$."

Answer 2

By definition, $$ |x-3| < 1 \quad\iff\quad -1 < x-3 < 1. $$ Now add $3$ throughout.