To solve an absolute value equation, the absolute value expression must first be isolated. For example, to solve $|5x - 4| - 3 = 8$, add $3$ to both sides to isolate the absolute value, yielding $|5x - 4| = 11$. Next, write the equivalent equations: $5x - 4 = -11$ and $5x - 4 = 11$. Solving each equation by adding $4$ and dividing by $5$ gives the solutions $x = -\frac{7}{5}$ and $x = 3$. Both solutions should be checked by substituting them back into the original equation to verify they are valid.