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