1:2 7/9=x+4 2/5x решите пожалуйста

1 : 2 7/9 = х + 4 2/5х 1 : 25/9 = х + 22/5х 1 * 9/25 = 5/5х + 22/5х 9/25 = 27/5х х = 9/25 : 27/5 х = 9/25 * 5/27 х = 1/5 * 1/3 х = 1/8

[latex]1: 2 \frac{7}{9} = x+4 \frac{2}{5}x \\ \\ x(1+ 4 \frac{2}{5}) = 1 : \frac{25}{9} \\ \\ 5 \frac{2}{5}x= 1* \frac{9}{25} \\ \\ x= \frac{9}{25} :5 \frac{2}{5} \\ \\ x= \frac{9*5}{25*27} = \frac{1*1}{5*3} \\ \\ x= \frac{1}{15} [/latex] Проверим: [latex]1: 2 \frac{7}{9} = \frac{1}{15} +4 \frac{2}{5}* \frac{1}{15} \\ \\ 1* \frac{9}{25} = \frac{1}{15} + \frac{22*1}{5*15} \\ \\ \frac{9}{25} = \frac{5}{75} + \frac{22}{75} \\ \\ \frac{9}{25} = \frac{27}{75} \\ \\ \frac{9}{25} = \frac{9}{25} [/latex]