Solve the following equations: a) \(\frac{x - 0.7}{x + 0.3} = \frac{5.7}{4.7}\) b) \(\frac{19.5}{x - 2.4} = \frac{47.25}{x + 1.3}\) B) \(\frac{x + 0.15}{4.1} = \frac{x - 2.4}{2.4}\) Г) \(\frac{2x - 4.16}{2.4} = \frac{5x - 6.16}{0.7}\)

Решение:

а)

\(\frac{x - 0.7}{x + 0.3} = \frac{5.7}{4.7}\)

\(4.7(x - 0.7) = 5.7(x + 0.3)\)

\(4.7x - 3.29 = 5.7x + 1.71\)

\(4.7x - 5.7x = 1.71 + 3.29\)

\(-1x = 5\)

\(x = -5\)

б)

\(\frac{19.5}{x - 2.4} = \frac{47.25}{x + 1.3}\)

\(19.5(x + 1.3) = 47.25(x - 2.4)\)

\(19.5x + 25.35 = 47.25x - 113.4\)

\(25.35 + 113.4 = 47.25x - 19.5x\)

\(138.75 = 27.75x\)

\(x = \frac{138.75}{27.75} = 5\)

В)

\(\frac{x + 0.15}{4.1} = \frac{x - 2.4}{2.4}\)

\(2.4(x + 0.15) = 4.1(x - 2.4)\)

\(2.4x + 0.36 = 4.1x - 9.84\)

\(0.36 + 9.84 = 4.1x - 2.4x\)

\(10.2 = 1.7x\)

\(x = \frac{10.2}{1.7} = 6\)

Г)

\(\frac{2x - 4.16}{2.4} = \frac{5x - 6.16}{0.7}\)

\(0.7(2x - 4.16) = 2.4(5x - 6.16)\)

\(1.4x - 2.912 = 12x - 14.784\)

\(14.784 - 2.912 = 12x - 1.4x\)

\(11.872 = 10.6x\)

\(x = \frac{11.872}{10.6} = 1.12\)

Ответ: а) \(x = -5\), б) \(x = 5\), В) \(x = 6\), Г) \(x = 1.12\).