Розв’яжи рівняння:
Розв'язок:
1) $-\frac{9}{44}x = -2\frac{5}{11}$
$x = -2\frac{5}{11} : \left(-\frac{9}{44}\right)$
$x = -\frac{27}{11} \cdot \left(-\frac{44}{9}\right)$
$x = \frac{27 \cdot 44}{11 \cdot 9}$
$x = 3 \cdot 4$
$x = 12$
Перевірка: $-\frac{9}{44} \cdot 12 = -\frac{9 \cdot 3}{11} = -\frac{27}{11} = -2\frac{5}{11}$
2) $1\frac{1}{5}x = -2\frac{7}{10}$
$x = -2\frac{7}{10} : 1\frac{1}{5}$
$x = -\frac{27}{10} : \frac{6}{5}$
$x = -\frac{27}{10} \cdot \frac{5}{6}$
$x = -\frac{9 \cdot 1}{2 \cdot 2}$
$x = -\frac{9}{4}$
$x = -2\frac{1}{4}$ (або $-2{,}25$)
Перевірка: $\frac{6}{5} \cdot \left(-\frac{9}{4}\right) = -\frac{3 \cdot 9}{5 \cdot 2} = -\frac{27}{10} = -2\frac{7}{10}$
3) $1\frac{1}{63} : x = -\frac{8}{21}$
$x = 1\frac{1}{63} : \left(-\frac{8}{21}\right)$
$x = \frac{64}{63} \cdot \left(-\frac{21}{8}\right)$
$x = -\frac{64 \cdot 21}{63 \cdot 8}$
$x = -\frac{8 \cdot 1}{3 \cdot 1}$
$x = -\frac{8}{3}$
$x = -2\frac{2}{3}$
Перевірка: $\frac{64}{63} : \left(-\frac{8}{3}\right) = \frac{64}{63} \cdot \left(-\frac{3}{8}\right) =$
$=-\frac{8 \cdot 1}{21 \cdot 1} = -\frac{8}{21}$
4) $\frac{8}{21}x = -3\frac{3}{7}$
$x = -3\frac{3}{7} : \frac{8}{21}$
$x = -\frac{24}{7} \cdot \frac{21}{8}$
$x = -\frac{24 \cdot 21}{7 \cdot 8}$
$x = -3 \cdot 3$
$x = -9$
Перевірка: $\frac{8}{21} \cdot (-9) = -\frac{8 \cdot 3}{7} = -\frac{24}{7} = -3\frac{3}{7}$
5) $-2\frac{5}{6} : x = -\frac{17}{18}$
$x = -2\frac{5}{6} : \left(-\frac{17}{18}\right)$
$x = -\frac{17}{6} \cdot \left(-\frac{18}{17}\right)$
$x = \frac{17 \cdot 18}{6 \cdot 17}$
$x = 3$
Перевірка: $-\frac{17}{6} : 3 = -\frac{17}{6 \cdot 3} = -\frac{17}{18}$
6) $1\frac{11}{14} : x = -2\frac{1}{7}$
$x = 1\frac{11}{14} : \left(-2\frac{1}{7}\right)$
$x = \frac{25}{14} : \left(-\frac{15}{7}\right)$
$x = \frac{25}{14} \cdot \left(-\frac{7}{15}\right)$
$x = -\frac{25 \cdot 7}{14 \cdot 15}$
$x = -\frac{5 \cdot 1}{2 \cdot 3}$
$x = -\frac{5}{6}$
Перевірка: $\frac{25}{14} : \left(-\frac{5}{6}\right) = \frac{25}{14} \cdot \left(-\frac{6}{5}\right) =$
$= -\frac{5 \cdot 3}{7 \cdot 1} = -\frac{15}{7} = -2\frac{1}{7}$