Question

Решить уравнение . 3/2х-2*(1/2+1/4х)=4х-6

Answer 1

$\frac{3}{2} x-2( \frac{1}{2} + \frac{1}{4}x) =4x-6 \\ \\ \frac{3}{2} x - 1 - \frac{1}{2} x= 4x-6 \\ \\ x-1=4x-6$
x-4x=-6+1
-3x= -5
x=(-5):(-3) =$\frac{5}{3}$
х=$1 \frac{2}{3}$

проверим:
$\frac{3}{2} * 1 \frac{2}{3} -2( \frac{1}{2} + \frac{1}{4}*1 \frac{2}{3} ) =4*1 \frac{2}{3} -6 \\ \\ \frac{3}{2} * \frac{5}{3} -2( \frac{1}{2} + \frac{1}{4}* \frac{5}{3} ) =4* \frac{5}{3} -6 \\ \\ \frac{5}{2} - 2 ( \frac{6}{12} + \frac{5}{12} )= \frac{20}{3} -6 \\ \\ \frac{5}{2} - \frac{2*11}{1*12} = 6 \frac{2}{3} -6 \\ \\ \frac{15}{6} - \frac{11}{6} = \frac{2}{3} \\ \\ \frac{4}{6} = \frac{2}{3} \\ \\ \frac{2}{3}= \frac{2}{3}$