Solving │ax + b│ = │cx + d│
To solve an absolute value equation of the form
│ax + b│ = │cx + d│,
Solve the compound equation
ax + b = cx + d or ax + b = – (cx + d).
Special Cases for Absolute Value
1. The absolute value of an expression can never be negative: │a│ ≥ 0 for all real numbers a.
2. The absolute value of an expression equals 0 only when the expression is equal to 0.