[tex]\dfrac{x-2}{3} =\dfrac{2x+7}{5} \ \ \ \ \ |\cdot15\\\\\not\!\!15^{5}\cdot\dfrac{x-2}{\not3} =\ \not\!\!15^{3}\cdot\dfrac{2x+7}{\not5} \\\\5\cdot(x-2)=3\cdot(2x+7)\\\\5\cdot x+5\cdot(-2)=3\cdot2x+3\cdot7\\\\5x-10=6x+21 \ \ \ \ \ \ |+10\\\\5x-10+10=6x+21+10\ \ \ \ \ | -6x\\\\5x-6x=6x-6x+31\\\\-x=31\ \ \ \ \ \ |:(-1)\\\\\boxed{x=-31}[/tex]
