$$ \begin{aligned} z+\frac{5}{3} &= \frac{1}{4}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12z+12\cdot\frac{5}{3} &= 12\cdot\frac{1}{4}&& \text{cancel out the denominators} \\[1 em]12z+20 &= 3&& \text{ move 20 to the right } \\[1 em]12z &= 3-20&& \\[1 em]12z &= -17&& \text{ divide both sides by $ 12 $ } \\[1 em]z &= -\frac{17}{12}&& \\[1 em] \end{aligned} $$

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