Solving Absolute Value Equations
Core rules for equations of the form |ax + b| = c:
c > 0
Two Solutions
Split into positive and negative cases: ax + b = c and ax + b = -c.
c = 0
One Solution
Single equation: ax + b = 0 with root x = -b / a.
c < 0
No Solution
Absolute value is always non-negative (|x| ≥ 0), so no real solutions exist.