[tex]a+1\dfrac{3}{4} = 4\dfrac{1}{6} \\ \\ a+\dfrac{1\cdot 4+3}{4} = \dfrac{4\cdot 6+1}{6}\\ \\ a +\dfrac{7}{4} = \dfrac{25}{6} \Big|\cdot 12 \\ \\ 12a+3\cdot 7 = 2\cdot 25 \\ \\ 12a+21 = 50 \\ \\ 12a = 50-21\\ \\ 12a = 29 \\ \\\Rightarrow \boxed{ a = \dfrac{29}{12} }[/tex]
