Решите уравнение:
а)

\frac{1}{3} (x + 1) - \frac{2}{3} (x - 1) = \frac{2}{3} (x - 3)

;
б)

\frac{1}{2} (3 x + 7) - \frac{3}{4} (2 x - 2) = \frac{3}{4} (x + 1)

;
в) x(x − 3) + x(2x − 1) = 3x(x − 2) − 3;
г) 3 + 2x(3x − 4) = 4x(2x + 5) − 2x(x − 1);
д) x(x + 1)(x − 10) = (x − 1)(x − 3)(x − 5);
е)

(x - 1) (x - 4) (x + 7) = x (x + 1)^{2}

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ГДЗ учебник по алгебре 7 класс Дорофеев. 7.3 Умножение одночлена на многочлен. Номер №696

\frac{1}{3} (x + 1) - \frac{2}{3} (x - 1) = \frac{2}{3} (x - 3)

\frac{1}{3} x + \frac{1}{3} - \frac{2}{3} x + \frac{2}{3} = \frac{2}{3} x - 2

- \frac{1}{3} x - \frac{2}{3} x = - 2 - \frac{3}{3}

- \frac{3}{3} x = - 3

−x = −3
x = 3

\frac{1}{2} (3 x + 7) - \frac{3}{4} (2 x - 2) = \frac{3}{4} (x + 1)

\frac{3}{2} x + \frac{7}{2} - \frac{3}{2} x + \frac{3}{2} = \frac{3}{4} x + \frac{3}{4}

\frac{3}{2} x - \frac{3}{2} x - \frac{3}{4} x = \frac{3}{4} - \frac{7}{2} - \frac{3}{2}

- \frac{3}{4} x = \frac{3}{4} - \frac{14}{4} - \frac{6}{4}

- \frac{3}{4} x = \frac{3}{4} - \frac{14}{4} - \frac{6}{4}

- \frac{3}{4} x = - \frac{17}{4}

x = \frac{17}{4} : \frac{3}{4}

x = \frac{17}{4} * \frac{4}{3}

x = \frac{17}{3} = 5 \frac{2}{3}

x(x − 3) + x(2x − 1) = 3x(x − 2) − 3

x^{2} - 3 x + 2 x^{2} - x = 3 x^{2} - 6 x - 3

3 x^{2} - 4 x - 3 x^{2} + 6 x = - 3

2x = −3
x = −1,5

3 + 2x(3x − 4) = 4x(2x + 5) − 2x(x − 1)

3 + 6 x^{2} - 8 x = 8 x^{2} + 20 x - 2 x^{2} + 2 x

6 x^{2} - 8 x^{2} + 2 x^{2} - 8 x - 20 x - 2 x = - 3

−30x = −3
x = 0,1

x(x + 1)(x − 10) = (x − 1)(x − 3)(x − 5)

x (x^{2} + x - 10 x - 10) = (x^{2} - x - 3 x + 3) (x - 5)

x (x^{2} - 9 x - 10) = (x^{2} - 4 x + 3) (x - 5)

x^{3} - 9 x^{2} - 10 x = x^{3} - 4 x^{2} + 3 x - 5 x^{2} + 20 x - 15

x^{3} - 9 x^{2} - 10 x - x^{3} + 4 x^{2} - 3 x + 5 x^{2} - 20 x = - 15

−33x = −15

x = \frac{15}{33} = \frac{5}{11}

(x - 1) (x - 4) (x + 7) = x (x + 1)^{2}

(x^{2} - x - 4 x + 4) (x + 7) = x (x^{2} + 2 x + 1)

(x^{2} - 5 x + 4) (x + 7) = x^{3} + 2 x^{2} + x

x^{3} - 5 x^{2} + 4 x + 7 x^{2} - 35 x + 28 = x^{3} + 2 x^{2} + x

x^{3} - 5 x^{2} + 4 x + 7 x^{2} - 35 x - x^{3} - 2 x^{2} - x = - 28

−32x = −28

x = \frac{28}{32} = \frac{7}{8}

ГДЗ Алгебра 7 класс Дорофеев, Суворова, Бунимович