Решение:
а) $x + 3 = 3x - 7$
$x - 3x = -7 - 3$
$-2x = -10$
$x = \frac{-10}{-2} = 5;$
б) $3 - x = 1 + x$
$-x - x = 1 - 3$
$-2x = -2$
$x = \frac{-2}{-2} = 1;$
в) $7x + 2 = 3x - 10$
$7x - 3x = -10 - 2$
$4x = -12$
$x = \frac{-12}{4} = -3;$
г) $5x - 8 = 3x - 8$
$5x - 3x = -8 + 8$
$8x = 0$
$x = \frac{0}{8} = 0;$
д) $\frac{1}{2}x - 3 = 2 - \frac{1}{3}x$
$\frac{1}{2}x + \frac{1}{3}x = 2 + 3$
$\frac{3 + 2}{6}x = 5$
$x = 5 : \frac{5}{6} = 5 * \frac{6}{5} = 6;$
е) $5x - 2\frac{1}{4} = \frac{1}{2}x$
$5x - \frac{1}{2}x = 2\frac{1}{4}$
$4\frac{1}{2}x = 2\frac{1}{4}$
$x = 2\frac{1}{4} : 4\frac{1}{2} = \frac{9}{4} * \frac{2}{9} = \frac{1}{2};$
ж) $\frac{2}{5}x - 1 = \frac{3}{4}x - 6$
$\frac{2}{5}x - \frac{3}{4}x = -6 + 1$
$4\frac{8 - 15}{20}x = -5$
$x = -5 : -\frac{7}{20} = -5 * -\frac{20}{7} = \frac{100}{7} = 14\frac{2}{7};$
з) $2x - \frac{3}{5} = \frac{3}{4}x - \frac{1}{2}$
$2x - \frac{3}{4}x = -\frac{1}{2} + \frac{3}{5}$
$1\frac{1}{4}x = \frac{-5 + 6}{10}$
$x = \frac{1}{10} : 1\frac{1}{4} = \frac{1}{10} * \frac{4}{5} = \frac{1 * 2}{5 * 5} = \frac{2}{25}.$
Ответ:
а) $5;$
б) $1;$
в) $-3;$
г) $0;$
д) $6;$
е) $\frac{1}{2};$
ж) $14\frac{2}{7};$
з) $\frac{2}{25}.$