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

$\frac{1}{2}(3x + 7) - \frac{3}{4}(2x - 2) = \frac{3}{4}(x + 1)$
$\frac{3}{2}x + \frac{7}{2} - \frac{3}{2}x + \frac{3}{2} = \frac{3}{4}x + \frac{3}{4}$
$\frac{3}{2}x - \frac{3}{2}x - \frac{3}{4}x = \frac{3}{4} - \frac{7}{2} - \frac{3}{2}$
$-\frac{3}{4}x = \frac{3}{4} - \frac{14}{4} - \frac{6}{4}$
$-\frac{3}{4}x = \frac{3}{4} - \frac{14}{4} - \frac{6}{4}$
$-\frac{3}{4}x = -\frac{17}{4}$
$x = \frac{17}{4} : \frac{3}{4}$
$x = \frac{17}{4} * \frac{4}{3}$
$x = \frac{17}{3} = 5\frac{2}{3}$

x(x − 3) + x(2x − 1) = 3x(x − 2) − 3
$x^2 - 3x + 2x^2 - x = 3x^2 - 6x - 3$
$3x^2 - 4x - 3x^2 + 6x = -3$
2x = −3
x = −1,5

3 + 2x(3x − 4) = 4x(2x + 5) − 2x(x − 1)
$3 + 6x^2 - 8x = 8x^2 + 20x - 2x^2 + 2x$
$6x^2 - 8x^2 + 2x^2 - 8x - 20x - 2x = -3$
−30x = −3
x = 0,1

x(x + 1)(x − 10) = (x − 1)(x − 3)(x − 5)
$x(x^2 + x - 10x - 10) = (x^2 - x - 3x + 3)(x - 5)$
$x(x^2 - 9x - 10) = (x^2 - 4x + 3)(x - 5)$
$x^3 - 9x^2 - 10x = x^3 - 4x^2 + 3x - 5x^2 + 20x - 15$
$x^3 - 9x^2 - 10x - x^3 + 4x^2 - 3x + 5x^2 - 20x = -15$
−33x = −15
$x = \frac{15}{33} = \frac{5}{11}$

$(x - 1)(x - 4)(x + 7) = x(x + 1)^2$
$(x^2 - x - 4x + 4)(x + 7) = x(x^2 + 2x + 1)$
$(x^2 - 5x + 4)(x + 7) = x^3 + 2x^2 + x$
$x^3 - 5x^2 + 4x + 7x^2 - 35x + 28 = x^3 + 2x^2 + x$
$x^3 - 5x^2 + 4x + 7x^2 - 35x - x^3 - 2x^2 - x = -28$
−32x = −28
$x = \frac{28}{32} = \frac{7}{8}$