If isolating the absolute value expression results in an equation where the absolute value equals a negative number, the equation possesses no solution. For example, to solve $|\frac{2}{3}x - 4| + 11 = 3$, isolating the absolute value by subtracting $11$ from both sides yields $|\frac{2}{3}x - 4| = -8$. Because the distance represented by an absolute value can never be negative, this statement is mathematically false for any value of $x$. Thus, finding it equal to a negative constant immediately indicates that there is no solution.