[tex]\dfrac{5}{3}=\dfrac{23}{6}n+\dfrac{7}{4}-\dfrac{7}{2}n\\\\LCM(2,\ 3,\ 4,\ 6)=12\\\\\dfrac{5}{3}=\dfrac{23}{6}n+\dfrac{7}{4}-\dfrac{7}{2}n\ \ \ \ |\cdot12\\\\12\cdot\dfrac{5}{3}=12\cdot\dfrac{23}{6}n+12\cdot\dfrac{7}{4}-12\cdot\dfrac{7}{2}n\\\\4\cdot5=2\cdot23n+3\cdot7-6\cdot7n\\\\20=46n+21-42n\\\\20=4n+21\ \ \ \ |-21\\\\-1=4n\ \ \ \ |:4\\\\\boxed{n=-\dfrac{1}{4}}[/tex]
