`(1)` `\frac{3}{4}x - (0,5x + \frac{1}{2}) = 15\%`

`\frac{3}{4}x - \frac{1}{2}x - \frac{1}{2} = \frac{3}{20}`

`\(\frac{3}{4} - \frac{2}{4})x = \frac{3}{20} + \frac{1}{2}`

`\frac{1}{4}x = \frac{3}{20} + \frac{10}{20}`

`\frac{1}{4}x = \frac{13}{20}`

`x = \frac{13}{20} \cdot 4`

`x = \frac{13}{5} = 2,6`

`(2)` `1\frac{1}{4} + \ (20\%x - \frac{3}{5}\ ) = 0,75x + \frac{1}{2}`

`\frac{5}{4} + \frac{1}{5}x - \frac{3}{5} = \frac{3}{4}x + \frac{1}{2}`

`\ (\frac{5}{4} - \frac{3}{5}\ ) + \frac{1}{5}x = \frac{3}{4}x + \frac{1}{2} `

`\frac{13}{20} + \frac{1}{5}x = \frac{3}{4}x + \frac{10}{20}`

`\frac{13}{20} - \frac{10}{20} = \frac{3}{4}x - \frac{1}{5}x`

`\frac{3}{20} = \ (\frac{15}{20} - \frac{4}{20}\ )x `

`\frac{3}{20} = \frac{11}{20}x`

`x = \frac{3}{11}`

`(3)` `0,6x - \ (x - \frac{3}{8}\ ) = 25\%x - 1,125`

`0,6x - x + 0,375 = 0,25x - 1,125`

`-0,4x + 0,375 = 0,25x - 1,125`

`0,375 + 1,125 = 0,25x + 0,4x`

`1,5 = 0,65x`

`x = \frac{1,5}{0,65} = \frac{30}{13}`

`(4)` `-\ (1,5x - 1\frac{1}{3}\ ) + 25\% = \frac{1}{2}x - 1,25`

`-1,5x + \frac{4}{3} + 0,25 = 0,5x - 1,25`

`\frac{4}{3} + 0,25 + 1,25 = 0,5x + 1,5x`

`\frac{4}{3} + 1,5 = 2x `

`\frac{4}{3} + \frac{3}{2} = 2x`

`\frac{17}{6} = 2x`

`x = \frac{17}{12}`

`(5)` `150\%x - \ (2,4 - \frac{1}{2}x\ ) = 3\frac{1}{5} + 0,1x`

`1,5x - 2,4 + 0,5x = 3,2 + 0,1x `

` 2x - 2,4 = 3,2 + 0,1x`

`2x - 0,1x = 3,2 + 2,4`

`1,9x = 5,6`

`x = \frac{5,6}{1,9} = \frac{56}{19}`

`(6)` `\frac{2}{3}x - (0,75x + 2) = -1\frac{1}{6} - \ (25\% - \frac{1}{4}x\ )`

`\frac{2}{3}x - \frac{3}{4}x - 2 = -\frac{7}{6} - \frac{1}{4} + \frac{1}{4}x`

`-\frac{1}{12}x - 2 = -\frac{17}{12} + \frac{1}{4}x`

`-\frac{1}{12}x - \frac{3}{12}x = -\frac{17}{12} + 2`

`-\frac{4}{12}x = \frac{7}{12}`

`-\frac{1}{3}x = \frac{7}{12}`

`x = \frac{7}{12} \cdot (-3) = -\frac{7}{4}`