d)
[tex]\frac{x-3}{2} = \frac{x-2}{3} \ \ |\cdot6\\\\6\cdot\frac{x-2}{2} = 6\cdot\frac{x-2}{3}\\\\3(x-3) = 2(x-2)\\\\3x-9 = 2x-4\\\\3x-2x = -4+9\\\\\boxed{x = 5}[/tex]
e)
[tex]\frac{x+1}{3} = \frac{1-2x}{4} \ \ |\cdot12\\\\12\cdot\frac{x+1}{3} = 12\cdot\frac{1-2x}{4}\\\\4(x+1) = 3(1-2x)\\\\4x+4 = 3-6x\\\\4x+6x = 3-4\\\\10x=-1 \ \ /:10\\\\\boxed{x = -\frac{1}{10}}[/tex]
f)
[tex]\frac{x+2}{6}=\frac{-x+3}{8} \ \ |\cdot24\\\\24\cdot\frac{x+2}{6} = 24\cdot\frac{-x+3}{8}\\\\4(x+2) = 3(-x+3)\\\\4x+8 = -3x+9\\\\4x+3x = 9 - 8\\\\7x = 1 \ \ /:7\\\\\boxed{x = \frac{1}{7}}[/tex]
