Question

Решите уравнение
2/3 (1/3х-1/2) = 4х+2 1/2

Answer 1

$frac{2}{3} ( frac{1}{3}x - frac{1}{2} ) = 4x + 2 frac{1}{2} \ \ frac{2}{3}*frac{1}{3}x - frac{2}{3} *frac{1}{2}=4x + 2 frac{1}{2} \ \ frac{2}{9} x - frac{1}{3} = 4x + 2 frac{1}{2} \ \ frac{2}{9} x - 4x = 2 frac{1}{2} + frac{1}{3} \ \ - 3 frac{7}{9} x = 2 frac{3}{6} + frac{2}{6} \ \ x = 2 frac{5}{6} : ( - 3 frac{7}{9} ) = frac{17}{6} * ( - frac{9}{34} ) = - frac{1*3}{2*2}= - frac{3}{4} \ \ x = -0,75$

проверим: 
$frac{2}{3} ( frac{1}{3}*(-0.75) - frac{1}{2} ) = 4*(-0.75) + 2 frac{1}{2} \ \ frac{2}{3} ( frac{1}{3}* (-frac{3}{4} ) - frac{1}{2} ) = frac{4}{1} *(- frac{3}{4} ) + 2 frac{1}{2} \ \ frac{2}{3} ( - frac{1}{4} - frac{2}{4} ) = - 3 + 2 frac{1}{2} \ \ frac{2}{3} * (- frac{3}{4} ) = - frac{1}{2} \ \ - frac{1}{2} = - frac{1}{2}$