$$ \begin{aligned} 2x+\frac{5}{3}-\frac{2}{5}x+3 &= 120&& \text{multiply ALL terms by } \color{blue}{ 15 }. \\[1 em]15\cdot2x+15\cdot\frac{5}{3}-15\frac{2}{5}x+15\cdot3 &= 15\cdot120&& \text{cancel out the denominators} \\[1 em]30x+25-6x+45 &= 1800&& \text{simplify left side} \\[1 em]24x+70 &= 1800&& \text{ move 70 to the right } \\[1 em]24x &= 1800-70&& \\[1 em]24x &= 1730&& \text{ divide both sides by $ 24 $ } \\[1 em]x &= \frac{1730}{24}&& \\[1 em]x &= \frac{865}{12}&& \\[1 em] \end{aligned} $$

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