\[\boxed{\text{529\ (529).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[1)\ \frac{4x - 1}{12} - \frac{3x + 1}{8} =\]
\[= x + 1\ \ \ \ \ | \cdot 24\]
\[2 \cdot (4x - 1) - 3 \cdot (3x + 1) =\]
\[= 24 \cdot (x + 1)\]
\[8x - 2 - 9x - 3 = 24x + 24\]
\[- 25x = 29\]
\[x = - \frac{29}{25}\]
\[x = - 1\frac{4}{25}\]
\[Ответ:\ x = - 1\frac{4}{25}.\]
\[2)\ \frac{3x - 2}{9} - \frac{2x + 1}{6} =\]
\[= \frac{5 - x}{3}\ \ \ \ \ \ | \cdot 18\]
\[2 \cdot (3x - 2) - 3 \cdot (2x + 1) =\]
\[= 6 \cdot (5 - x)\]
\[6x - 4 - 6x - 3 = 30 - 6x\]
\[6x = 37\]
\[x = \frac{37}{6}\]
\[x = 6\frac{1}{6}\]
\[Ответ:x = 6\frac{1}{6}.\]
\[\boxed{\text{529.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
Пояснение.
Решение.
\[x = 8a + 3;\ \ y = 8b + 7:\]
\[xy = (8a + 3) \cdot (8b + 7) =\]
\[= 64ab + 56a + 24b + 21 =\]
\[= 8 \cdot (8ab + 7a + 3b) + 21.\]
\[8 \cdot (8ab + 7a + 3b) - делится\ \]
\[на\ 8;\]
\[21\ :8 = 2\ и\ остаток\ 5.\ \]
\[Что\ и\ требовалось\ доказать.\]