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Question 1

Question 2

#1.

$\frac{x-14}{x - 8} = \frac{7}{10} \\\\10 * (x-14) = 7 * (x-8)\\10x - 140 = 7x - 56\\10 x - 7x = 140 - 56\\3x = 84\\x = 28$

#2.

$6 + \frac{x}{2} = \frac{x+3}{5} \\\\\frac{12 +x}{2} = \frac{x+3}{5} \\\\5 * (12+x) = 2 * (x+3)\\60 + 5x = 2x + 6\\5x - 2x = 6 - 60\\3x = -54\\x = -18$

#3.

$\frac{x+7}{3} + \frac{x}{3} = 8\\\\\frac{x+7 + x}{3} = 8\\\\\frac{2x+7}{3} = \frac{8}{1} \\\\2x+7 = 8*3\\2x = 24 - 7\\x = 17 : 2 = 8,5$

#4.

$\frac{3x-2}{4} - \frac{x}{3} = 2\\\\\frac{3(3x-2) - 4*x}{4 * 3} = 2\\\\\frac{9x - 6 - 4x}{12} = \frac{2}{1} \\\\5x - 6 = 2 * 12\\5x = 24 + 6\\ 5x = 30\\x=6$

#5.

$\frac{1}{x+2} = -\frac{1}{2} \\\\1 * 2 = -1 * (x+2)\\2 = -x - 2\\ x = -4$

#6.

$x - \frac{6}{x} = -5\\\\\frac{x+5}{1} = \frac{6}{x} \\\\x(x+5) = 6\\x^2 + 5x - 6 = 0\\$

По теореме Виета:

$\left[\begin{array}{ccc}x_1 = -6\\x_2 = 1\end{array}\right$

Ответ: -6.

#7.

$\frac{x}{6} + \frac{x}{5} + x = -\frac{41}{6} \\\\\frac{5x +6x + 30x}{30} = -\frac{41}{6} \\\\\frac{41x}{30} = -\frac{41}{6} \\\\41x * 6 = 30 * (-41)|:41*6\\ x = 5 * (-1) = -5$