$1\frac{1}{3}x + 1\frac{5}{6} = 2\frac{2}{3} - 2\frac{1}{6}x$
$\frac{4}{3}x + \frac{13}{6}x = 2\frac{4}{6} - 1\frac{5}{6}$
$\frac{8}{6}x + \frac{13}{6}x = 1\frac{10}{6} - 1\frac{5}{6}$
$\frac{21}{6}x = \frac{5}{6}$
$x = \frac{5}{6} : \frac{21}{6}$
$x = \frac{5}{6} * \frac{6}{21}$
$x = \frac{5}{21}$

$2\frac{7}{15} - 3\frac{1}{5}x = 2\frac{1}{15}x - 1\frac{4}{5}$
$-2\frac{1}{15}x - 3\frac{3}{15}x = -1\frac{12}{15} - 2\frac{7}{15}$
$-5\frac{4}{15}x = -3\frac{19}{15}$
$-\frac{79}{15}x = -\frac{64}{15}$
$x = \frac{64}{15} : \frac{79}{15}$
$x = \frac{64}{15} * \frac{15}{79}$
$x = \frac{64}{79}$

$7\frac{1}{4}x - 3\frac{3}{8} = 5\frac{1}{8}x + 5\frac{3}{4}$
$7\frac{2}{8}x - 5\frac{1}{8}x = 5\frac{6}{8} + 3\frac{3}{8}$
$2\frac{1}{8}x = 8\frac{9}{8}$
$\frac{17}{8}x = \frac{73}{8}$
$x = \frac{73}{8} : \frac{17}{8}$
$x = \frac{73}{8} * \frac{8}{17}$
$x = \frac{73}{17} = 4\frac{5}{17}$

$1\frac{1}{21}x + 4\frac{1}{3} = 2\frac{5}{21} + 3\frac{1}{7}x$
$1\frac{1}{21}x - 3\frac{3}{21}x = 2\frac{5}{21} - 4\frac{7}{21}$
$-2\frac{2}{21}x = -2\frac{2}{21}$
x = 1