Question

Solve the equation. | 2z - 3| = 4z - 1

Answer 1

Keeping in mind that, an absolute value expression is in effect a piece-wise, then

$\bf |2z-3|=4z-1\implies \begin{cases} +(2z-3)=4z-1\\ \qquad 2z-3=4z-1\\ \qquad -2=2z\\ \qquad \frac{-2}{2}=z\\ \qquad -1=z\\ ----------\\ -(2z-3)=4z-1\\ \qquad -2z+3=4z-1\\ \qquad 4=6z\\ \qquad \frac{4}{6}=z\\\\ \qquad \frac{2}{3}=z \end{cases}$