a)
[tex] \frac{x}{2} = \frac{5}{6} \\ 6x = 10 \\ x = \frac{10}{6} \\ x = 1 \frac{2}{3} [/tex]
b)
[tex] \frac{x}{2} = \frac{x + 1}{4} \\ 4x = 2(x + 1) \\ 4x = 2x + 2 \\ 4x - 2x = 2 \\ 2x = 2 \\ x = 1[/tex]
c)
[tex] \frac{2(x - 1)}{3} = \frac{x + 2}{5} \\ \frac{2x - 2}{3} = \frac{x + 2}{5} \\ 5(2x - 2) = 3(x + 2) \\ 10x - 10 = 3x + 6 \\ 10x - 3x = 6 + 10 \\ 7x = 16 \\ x = \frac{16}{7} \\ x = 2 \frac{2}{7} [/tex]
d)
[tex]1 - \frac{2x + 5}{3} = 4 \\ 3 - 2x + 5 = 12 \\ - 2x = 12 + 3 - 5 \\ - 2x = 10 \\ 2x = - 10 \\ x = - 5[/tex]
e)
[tex] \frac{x}{2} - \frac{x}{3} + 1 = \frac{1}{6} (x + 6) \\ 3x - 2x + 1 = \frac{1}{6} x + 1 \\ x - \frac{1}{6} x = 0 \\ \frac{5}{6} x = 0 \\ 5x = 0 \\ x = 0[/tex]
f)
[tex] \frac{x - 1}{4} - \frac{x + 1}{2} = - \frac{x}{4} \\ x - 1 - 2x + 2 = - x \\ x - 2x + x = - 2 + 1 \\ 0 = 1[/tex]
równanie sprzeczne
