Question

solve |x - 12| - 3 = 11.

Explanation:

Step1: Isolate the absolute - value term

Add 3 to both sides of the equation $|x - 12|-3 = 11$.
$|x - 12|=11 + 3$
$|x - 12|=14$

Step2: Consider two cases

Case 1: $x-12 = 14$. Solve for $x$ by adding 12 to both sides.
$x=14 + 12$
$x = 26$
Case 2: $x - 12=-14$. Solve for $x$ by adding 12 to both sides.
$x=-14 + 12$
$x=-2$

Answer:

$x = 26$ or $x=-2$