Question

$|x-3| + 5 = 11$

Explanation:

Step1: Isolate the absolute value

Subtract 5 from both sides.
$$|x-3| + 5 - 5 = 11 - 5$$
$$|x-3| = 6$$

Step2: Split into two linear equations

Absolute value equals positive/negative 6.
$$x-3 = 6 \quad \text{or} \quad x-3 = -6$$

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 $x = -3$