h)
[tex]x-2 = \frac{x}{3}-\frac{1}{3} \ \ /\cdot3\\\\3x-6 = x-1\\\\3x-x = -1+6\\\\2x = 5 \ \ /:2\\\\\underline{x = 2\frac{1}{2}}[/tex]
i)
[tex]2x-\frac{3\cdot(x+1)}{2} = x \ \ /\cdot2\\\\4x-3(x+1) = 2x\\\\4x-3x-3 = 2x\\\\x-2x = 3\\\\-x = 3 \ \ /:(-1)\\\\\underline{x = -3}[/tex]
j)
[tex]\frac{x}{3}+\frac{2x}{5}-\frac{3x}{7} = \frac{6}{105} \ \ /\cdot105\\\\35x + 21\cdot2x-15\cdot3x=6\\\\35x+42x-45x = 6\\\\32x = 6 \ \ /:2\\\\16x = 3 \ \ /:16\\\\\underline{x = \frac{3}{16}}[/tex]
k)
[tex]7x^{2}+4x=3x^{2}\\\\7x^{2}-3x^{2}+4x = 0\\\\4x^{2}+4x = 0\\\\4x(x+1) = 0 \ \ /:4\\\\x(x+1) = 0\\\\x = 0 \ \vee \ x+1 = 0\\\\x = 0 \ \vee \ x = -1\\\\\underline{x \in \{-1, 0\}}[/tex]
l)
[tex]\frac{1}{4}x^{3}-\frac{1}{4} = \frac{1}{4}x^{2}-\frac{1}{4} \ \ /\cdot4\\\\x^{3}-1 = x^{2}-1\\\\x^{3}-x^{2} = -1+1\\\\x^{2}(x-1) = 0\\\\x^{2} = 0 \ \vee \ x-1 = 0\\\\x = 0 \ \vee \ x = 1\\\\\underline{x \in \{0, 1\}}[/tex]
