Question

1. $|x - 3| - 2 > -1$

Explanation:

Step1: Isolate the absolute value

Add 2 to both sides.
$$|x-3| - 2 + 2 > -1 + 2$$
$$|x-3| > 1$$

Step2: Split into two inequalities

For $|A|>b$, solve $A>b$ and $A<-b$.
$$x-3 > 1 \quad \text{or} \quad x-3 < -1$$

Step3: Solve each inequality

Solve $x-3>1$: add 3 to both sides.
$$x > 1 + 3$$
$$x > 4$$
Solve $x-3<-1$: add 3 to both sides.
$$x < -1 + 3$$
$$x < 2$$

Answer:

$x < 2$ or $x > 4$
(On a number line: open circles at 2 and 4, shade to the left of 2 and to the right of 4)