When an absolute value equation contains extra terms, apply algebraic properties to completely isolate the absolute value expression before splitting it into two equations. For example, to solve $2|x - 7| + 5 = 9$, first subtract $5$ from both sides to obtain $2|x - 7| = 4$. Next, divide by $2$ to yield the isolated equation $|x - 7| = 2$. Then, formulate the equivalent equations: $x - 7 = -2$ or $x - 7 = 2$. Solving each produces $x = 5$ or $x = 9$. Finally, substituting both values back into the initial equation verifies that both $x = 5$ and $x = 9$ are valid solutions.