[tex]\dfrac{2a+3b}{3a+2b} = \dfrac{5}{11} \Rightarrow \dfrac{\dfrac{1}{b}\Big(2a+3b\Big)}{\dfrac{1}{b}\Big(3a+2b\Big)} =\dfrac{5}{11} \Rightarrow\dfrac{2\cdot \dfrac{a}{b}+3}{3\cdot \dfrac{a}{b}+2} = \dfrac{5}{11} \\ \\ \dfrac{a}{b} = x \Rightarrow \dfrac{2x+3}{3x+2} = \dfrac{5}{11} \Rightarrow 11(2x+3) = 5(3x+2) \Rightarrow \\ \\ \Rightarrow 22x+33 = 15x+10\Rightarrow 7x = -23 \Rightarrow x = -\dfrac{23}{7} \Rightarrow \boxed{\dfrac{a}{b} = - \dfrac{23}{7}}[/tex]
