$2\frac{2}{11}x - \frac{5}{16} = 1\frac{3}{4}$
$2\frac{2}{11}x = 1\frac{12}{16} + \frac{5}{16}$
$2\frac{2}{11}x = 2\frac{1}{16}$
$x = \frac{33}{16} : \frac{24}{11}$
$x = \frac{33}{16} * \frac{11}{24}$
$x = \frac{121}{128}$

$4\frac{2}{9}x + 3\frac{5}{14} = 6\frac{11}{21}$
$4\frac{2}{9}x = 6\frac{11}{21} - 3\frac{5}{14}$
$4\frac{2}{9}x = 6\frac{22}{42} - 3\frac{15}{42}$
$4\frac{2}{9}x = 3\frac{1}{6}$
$x = 3\frac{1}{6} : 4\frac{2}{9}$
$x = \frac{19}{6} : \frac{38}{9}$
$x = \frac{19}{6} * \frac{9}{38}$
$x = \frac{1}{2} * \frac{3}{2}$
$x = \frac{3}{4}$

$\frac{11}{18} - \frac{14}{27}x = \frac{5}{12}$
$\frac{14}{27}x = \frac{11}{18} - \frac{5}{12}$
$\frac{14}{27}x = \frac{22}{36} - \frac{15}{36}$
$\frac{14}{27}x = \frac{7}{36}$
$x = \frac{7}{36} : \frac{14}{27}$
$x = \frac{7}{36} * \frac{27}{14}$
$x = \frac{1}{4} * \frac{3}{2}$
$x = \frac{3}{8}$

$\frac{1}{3}x + \frac{1}{4}x + \frac{1}{5}x = 1\frac{19}{75}$
$\frac{20}{60}x + \frac{15}{60}x + \frac{12}{60}x = \frac{94}{75}$
$\frac{47}{60}x = \frac{94}{75}$
$x = \frac{94}{75} : \frac{47}{60}$
$x = \frac{94}{75} * \frac{60}{47}$
$x = \frac{2}{5} * \frac{4}{1}$
$x = \frac{8}{5} = 1\frac{3}{5}$

$4\frac{1}{2} : x + 1\frac{3}{4} = 3\frac{19}{28}$
$4\frac{1}{2} : x = 2\frac{47}{28} - 1\frac{21}{28}$
$4\frac{1}{2} : x = 1\frac{13}{14}$
$x = 4\frac{1}{2} : 1\frac{13}{14}$
$x = \frac{9}{2} : \frac{27}{14}$
$x = \frac{9}{2} * \frac{14}{27}$
$x = \frac{1}{1} * \frac{7}{3}$
$x = 2\frac{1}{3}$

$3\frac{2}{3} : (x - 2\frac{4}{15}) = 3\frac{5}{13}$
$x - 2\frac{4}{15} = 3\frac{2}{3} : 3\frac{5}{13}$
$x - 2\frac{4}{15} = \frac{11}{3} : \frac{44}{13}$
$x - 2\frac{4}{15} = \frac{11}{3} * \frac{13}{44}$
$x - 2\frac{4}{15} = \frac{1}{3} * \frac{13}{4}$
$x = 1\frac{1}{12} + 2\frac{4}{15}$
$x = 1\frac{5}{60} + 2\frac{16}{60}$
$x = 3\frac{21}{60} = 3\frac{7}{20}$