5.32 Решите уравнение: а) 9,6:3 = 3,6: (\frac{1}{4}x); б) 6 : (4x) = 2,6: 8\frac{2}{3}

Решение:

а) 9.6 : 3 = 3.6 : (\frac{1}{4}x) \[\frac{9.6}{3} = \frac{3.6}{\frac{1}{4}x}\] Используем основное свойство пропорции: \[9.6 \cdot (\frac{1}{4}x) = 3 \cdot 3.6\] \[2.4x = 10.8\] \[x = \frac{10.8}{2.4}\] \[x = 4.5\] \[x = \frac{4.5}{1}\] \[x = \frac{45}{10}\] \[x = \frac{9}{2}\] \[x = 4 \frac{1}{2}\] б) 6 : (4x) = 2.6 : 8\frac{2}{3} \[\frac{6}{4x} = \frac{2.6}{8\frac{2}{3}}\] \[\frac{6}{4x} = \frac{2.6}{\frac{26}{3}}\] \[\frac{6}{4x} = \frac{2.6 \cdot 3}{26}\] \[\frac{6}{4x} = \frac{7.8}{26}\] \[4x = \frac{6 \cdot 26}{7.8}\] \[4x = \frac{156}{7.8}\] \[4x = 20\] \[x = \frac{20}{4}\] \[x = 5\]