Question

Решите уравнения: а) x + 4/15 = 2/3 + 2/5 б) ( 4/5 - x ) + 13/20 = 25/30 в) y – 5/20 = 5/8 – 3/10 г) 2/3 – ( 7/9 – а ) = 1/3

Answer 1

$x + \frac{4}{15} = \frac{2}{3} + \frac{2}{5} \\ \\ x = \frac{2}{3} + \frac{2}{5}- \frac{4}{15} \\ \\ x = \frac{2*5+2*3-4}{15}=\frac{10+6-4}{15}=\frac{12}{15}= \frac{4}{5}$

$( \frac{4}{5} - x ) + \frac{13}{20} = \frac{25}{30} \\ \\ x = \frac{4}{5} + \frac{13}{20}-\frac{25}{30} \\ \\ x = \frac{4*12+13*3-25*2}{60}=\frac{48+39-50}{60}=\frac{37}{60} \\ \\$

$y - \frac{5}{20} = \frac{5}{8} - \frac{3}{10} \\ \\ y - \frac{1}{4} = \frac{5}{8} - \frac{3}{10} \\ \\ y = \frac{5}{8} - \frac{3}{10}+\frac{1}{4} \\ \\ y =\frac{5*5-3*4+1*10}{40}=\frac{25-12+10}{40}=\frac{23}{40} \\ \\$

$\frac{2}{3} -( \frac{7}{9} - a ) = \frac{1}{3} \\ \\ \frac{2}{3} - \frac{7}{9} + a = \frac{1}{3} \\ \\ a = \frac{1}{3} -\frac{2}{3}+\frac{7}{9} \\ \\ a = \frac{1*3-2*3+7}{9}=\frac{3-6+7}{9}= \frac{4}{9}$