№20. Реши уравнение, заданное пропорцией. a) 2,5x : 18 = 1/6 : 30; б) 4,5 : (16x) = 1/2 : 40; в) 3 3/4 : (2x) = 2,6 : 4; г) 2,4 : (4x) = 6 2/3 : 4 4/9; д) 2 2/5 : 2 1/4 = 0,2x : 3; е) 1,6x : 2 7/9 = 0,63 : 0,21.

a) \(2.5x : 18 = \frac{1}{6} : 30\) \(2.5x \cdot 30 = 18 \cdot \frac{1}{6}\) \(75x = 3\) \(x = \frac{3}{75}\) \(x = 0.04\) б) \(4.5 : 16x = \frac{1}{2} : 40\) \(4.5 \cdot 40 = 16x \cdot \frac{1}{2}\) \(180 = 8x\) \(x = \frac{180}{8}\) \(x = 22.5\) в) \(3\frac{3}{4} : 2x = 2.6 : 4\) или \(\frac{15}{4} : 2x = \frac{13}{5} : 4\) \(\frac{15}{4} \cdot 4 = 2x \cdot \frac{13}{5}\) \(15 = \frac{26}{5}x\) \(x = 15 \cdot \frac{5}{26}\) \(x = \frac{75}{26}\) или \(x = 2.88\) (приблизительно) г) \(2.4 : 4x = 6\frac{2}{3} : 4\frac{4}{9}\) или \(\frac{12}{5} : 4x = \frac{20}{3} : \frac{40}{9}\) \(\frac{12}{5} \cdot \frac{40}{9} = 4x \cdot \frac{20}{3}\) \(\frac{160}{3} = \frac{80}{3}x\) \(x = \frac{160}{3} \cdot \frac{3}{80}\) \(x=2\) д) \(2\frac{2}{5} : 2\frac{1}{4} = 0.2x : 3\) или \(\frac{12}{5} : \frac{9}{4} = \frac{1}{5}x : 3\) \(\frac{12}{5} \cdot 3 = \frac{9}{4} \cdot \frac{1}{5}x\) \(\frac{36}{5} = \frac{9}{20}x\) \(x = \frac{36}{5} \cdot \frac{20}{9}\) \(x = 16\) е) \(1.6x : 2\frac{7}{9} = 0.63 : 0.21\) или \(1.6x : \frac{25}{9} = \frac{63}{100} : \frac{21}{100}\) \(1.6x : \frac{25}{9} = 3\) \(1.6x \cdot \frac{21}{100} = \frac{25}{9} \cdot \frac{63}{100}\) \(1.6x \cdot \frac{21}{100} = \frac{175}{100}\) \(1.6x = \frac{175}{100} \cdot \frac{100}{21}\) \(1.6x = \frac{175}{21}\) \(1.6x = \frac{25}{3}\) \(x= \frac{25}{3} \cdot \frac{10}{16}\) \(x= \frac{125}{24}\) или \(x = 5.21\) (приблизительно) Ответ: a) x = 0.04; б) x = 22.5; в) x = 2.88 (приблизительно); г) x = 2; д) x = 16; е) x = 5.21 (приблизительно)