Question

14. Să se afle x, folosind proporții derivate: x +4 5 1 10 1313 b) x-1 3 a) d) X ∞|2|X 7,5 2 4 8 e) 11,5 x +4,5 2,5 x-4,5 c) f) x+2 1 - استاده آبی X 1- = 0,25; 2-x X​

Answer 1

Explicație pas cu pas:

$\dfrac{x + 4}{x} = \dfrac{5}{3} \iff \dfrac{x + 4 - x}{x} = \dfrac{5 - 3}{3} \\ \dfrac{4}{x} = \dfrac{2}{3} \iff x = \dfrac{12}{2} \implies x = 6$

$\dfrac{1}{x - 1} = \dfrac{10}{3} \iff \dfrac{1}{x - 1 + 1} = \dfrac{10}{3 + 10} \\ \dfrac{1}{x} = \dfrac{10}{13} \iff x = \dfrac{13}{10} \implies x = 1\dfrac{3}{10}$

$\dfrac{x + 2}{x} = 0.25 = \dfrac{25}{100} \iff \dfrac{x + 2}{x} = \dfrac{1}{4} \\ \dfrac{x + 2 - x}{x} = \dfrac{1 - 4}{4} \iff \dfrac{2}{x} = - \dfrac{3}{4} \\ x = - \dfrac{8}{3} \implies x = - 2\dfrac{2}{3}$

$\dfrac{7.5}{4} = \dfrac{\dfrac{x}{2}}{8} \iff \dfrac{75}{40} = \dfrac{x}{16} \\ x = \dfrac{75 \cdot 16}{40} \implies x = 30$

$\dfrac{11.5}{2.5} = \dfrac{x + 4.5}{x - 4.5} \\ \dfrac{11.5 - 2.5}{2.5} = \dfrac{x + 4.5 - (x - 4.5)}{x - 4.5} \\ \dfrac{9}{2.5} = \dfrac{x + 4.5 - x + 4.5}{x - 4.5} \\ \dfrac{9}{2.5} = \dfrac{9}{x - 4.5} \iff x - 4.5 = 2.5 \\ x = 2.5 + 4.5 \implies x = 7$

$\dfrac{\dfrac{1}{3}}{1\dfrac{2}{3}} = \dfrac{2 - x}{x} \iff \dfrac{\dfrac{1}{3}}{\dfrac{5}{3}} = \dfrac{2 - x}{x} \\ \dfrac{1}{5} = \dfrac{2 - x}{x} \iff \dfrac{1 + 5}{5} = \dfrac{2 - x + x}{x} \\ \dfrac{6}{5} = \dfrac{2}{x} \iff x = \dfrac{10}{6} \implies x = \dfrac{5}{3}$