Алгебра
Английский
Биология
География
Геометрия
История
Русский
Обществознание
Физика
Химия
Информатика
Литература
МатематикаРешебник по алгебре 7 класс Мерзляк Задание 375
Задание 375
\[\boxed{\text{375\ (375).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[1)\ \frac{x - 7^{\backslash 3}}{4} - \frac{x^{\backslash 2}}{6} = 2\]
\[\frac{3 \cdot (x - 7) - 2x}{12} = 2\ \ \ \ \ \ \ \ | \cdot 12\]
\[3x - 21 - 2x = 24\]
\[x = 24 + 21\]
\[x = 45.\]
\[Ответ:x = 45.\]
\[2)\ \frac{x + 6^{\backslash 7}}{2} - \frac{x - 7^{\backslash 2}}{7} = 4\]
\[\frac{7 \cdot (x + 6) - 2 \cdot (x - 7)}{14} =\]
\[= 4\ \ \ \ \ \ \ | \cdot 14\]
\[7x + 42 - 2x + 14 = 56\]
\[5x = 56 - 56\]
\[5x = 0\]
\[x = 0.\]
\[Ответ:x = 0.\]
\[3)\ \frac{2x + 3^{\backslash 4}}{6} + \frac{1 - 4x^{\backslash 3}}{8} = \frac{1}{3}\]
\[\frac{4 \cdot (2x + 3) + 3 \cdot (1 - 4x)}{24} =\]
\[= \frac{1}{3}\ \ \ \ \ | \cdot 24\]
\[8x + 12 + 3 - 12x = 8\]
\[- 4x = 8 - 15\]
\[- 4x = - 7\]
\[x = \frac{7}{4} = 1,25.\]
\[Ответ:\ \ x = 1,25.\]
\[4)\ 3x^{\backslash 2} - \frac{2x + 3}{2} = \frac{x + 6}{3}\]
\[\frac{6x - 2x - 3}{2} = \frac{x + 6}{3}\]
\[\frac{4x - 3}{2} = \frac{x + 6}{3}\ \ \ \ \ \ \ \ | \cdot 6\]
\[3 \cdot (4x - 3) = 2 \cdot (x + 6)\]
\[12x - 9 = 2x + 12\]
\[12x - 2 = 12 + 9\]
\[10x = 21\]
\[x = 2,1.\]
\[Ответ:x = 2,1.\]
\[5)\ \frac{6x - 7^{\backslash 6}}{5} - \frac{3x + 1^{\backslash 5}}{6} =\]
\[= \frac{11 - x}{15}\]
\[\frac{6 \cdot (6x - 7) - 5 \cdot (3x + 1)}{30} =\]
\[= \frac{11 - x}{15}\ \ \ \ \ \ | \cdot 30\]
\[36x - 42 - 15x - 5 =\]
\[= 2 \cdot (11 - x)\]
\[21x - 47 = 22 - 2x\]
\[21x + 2x = 22 + 47\]
\[23x = 69\]
\[x = 3.\]
\[Ответ:x = 3.\]
\[6)\ \frac{5x - 3}{9} - \frac{4x + 3}{6} =\]
\[= x - 1\ \ \ \ \ \ \ \ | \cdot 18\]
\[2 \cdot (5x - 3) - 3 \cdot (4x + 3) =\]
\[= 18 \cdot (x - 1)\]
\[10x - 6 - 12x - 9 = 18x - 18\]
\[- 2x - 18x = - 18 + 6 + 9\]
\[- 20x = - 3\]
\[x = \frac{3}{20}.\]
\[Ответ:x = \frac{3}{20}.\]
\[7)\ \frac{8x - 5}{3} - \frac{4x + 3}{4} + \frac{2 - 9x}{2} =\]
\[= - 3\ \ \ \ \ \ \ \ \ | \cdot 12\]
\[- 34x = - 36 + 20 + 9 - 12\]
\[- 34x = - 19\]
\[x = \frac{19}{34}.\]
\[Ответ:\ x = \frac{19}{34}.\]
\[8)\ \frac{8x^{2} - 3x}{16} - \frac{6x^{2} + 1}{12} =\]
\[= - 1\ \ \ \ \ \ \ \ \ | \cdot 48\]
\[3 \cdot \left( 8x^{2} - 3x \right) - 4 \cdot \left( 6x^{2} + 1 \right) =\]
\[= - 48\]
\[- 9x = - 48 + 4\]
\[- 9x = - 44\]
\[x = \frac{44}{9} = 4\frac{8}{9}\]
\[Ответ:\ x = 4\frac{8}{9}\text{.\ }\]
