870. Найдите число х, для которого верно равенство:

Решение:

а)

\( x + \frac{1}{8} = \frac{3}{5} \)

\( x = \frac{3}{5} - \frac{1}{8} \)

\( x = \frac{3 \cdot 8 - 1 \cdot 5}{5 \cdot 8} \)

\( x = \frac{24 - 5}{40} \)

\( x = \frac{19}{40} \)

б)

\( \frac{1}{3} + x = \frac{1}{5} \)

\( x = \frac{1}{5} - \frac{1}{3} \)

\( x = \frac{1 \cdot 3 - 1 \cdot 5}{5 \cdot 3} \)

\( x = \frac{3 - 5}{15} \)

\( x = -\frac{2}{15} \)

г)

\( x - \frac{3}{7} = \frac{4}{21} \)

\( x = \frac{4}{21} + \frac{3}{7} \)

\( x = \frac{4 + 3 \cdot 3}{21} \)

\( x = \frac{4 + 9}{21} \)

\( x = \frac{13}{21} \)

д)

\( \frac{4}{5} - x = \frac{1}{12} \)

\( x = \frac{4}{5} - \frac{1}{12} \)

\( x = \frac{4 \cdot 12 - 1 \cdot 5}{5 \cdot 12} \)

\( x = \frac{48 - 5}{60} \)

\( x = \frac{43}{60} \)

е)

\( \frac{5}{8} - x = \frac{1}{3} \)

\( x = \frac{5}{8} - \frac{1}{3} \)

\( x = \frac{5 \cdot 3 - 1 \cdot 8}{8 \cdot 3} \)

\( x = \frac{15 - 8}{24} \)

\( x = \frac{7}{24} \)

B)

\( x - \frac{3}{20} = \frac{1}{5} \)

\( x = \frac{1}{5} + \frac{3}{20} \)

\( x = \frac{1 \cdot 4 + 3}{20} \)

\( x = \frac{4 + 3}{20} \)

\( x = \frac{7}{20} \)

Ответ: а) \( \frac{19}{40} \), б) \( -\frac{2}{15} \), г) \( \frac{13}{21} \), д) \( \frac{43}{60} \), е) \( \frac{7}{24} \), B) \( \frac{7}{20} \).