Question

1. $|x - 3| - 4 = 2$

Explanation:

Step1: Isolate absolute value term

Add 4 to both sides.
$$|x-3| - 4 + 4 = 2 + 4$$
$$|x-3| = 6$$

Step2: Split into two linear equations

Apply absolute value rule: if $|A|=B$, then $A=B$ or $A=-B$.
$$x-3 = 6 \quad \text{or} \quad x-3 = -6$$

Step3: Solve first linear equation

Add 3 to both sides.
$$x = 6 + 3$$
$$x = 9$$

Step4: Solve second linear equation

Add 3 to both sides.
$$x = -6 + 3$$
$$x = -3$$

Answer:

$x=9$ or $x=-3$