Question

Решите уравнения 1) (x-7): 6=(x+1): 2-3 2) 1/2-(3x): 4=2(3-x): 5

Answer 1

( X - 7 ) : 6 = ( X + 1 ) : 2 - 3 
( X - 7 ) : 6 = ( X + 2 - 6 ) : 2 
2 * ( X - 7 ) = 3 * ( X - 4 ) 
2X - 14 = 3X - 12 
3X - 2X = - 14 + 12 
X = - 2 

1/2 - ( 3X ) : 4 = 2 * ( 3 - X ) : 5 
2/4 - ( 3X ) : 4 = ( 6 - 2X ) : 5 
5 * 2 - 5 * 3X = 4 * ( 6 - 2X ) 
10 - 15X = 24 - 8X 
15X - 8X = 10 - 24 
7X = - 14 
X = - 2 

Answer 2

1)
$(x-7):6=(x+1):2-3 \\ \\ \frac{x-7}{6}= \frac{x+1}{2}-3 \\ \\ \frac{x-7}{6}= \frac{3x+3}{6}- \frac{18}{6} \\ \\ x-3x=-15+7 \\ \\ -2x=-8 \\ \\ x=4$

2)
$\frac{1}{2}- (3x) :4 =2(3-x):5 \\ \\ \frac{1}{2}- \frac{3x}{4}= \frac{2(3-x)}{5} \\ \\ \frac{10}{20}- \frac{15x}{20} = \frac{24-8x}{20} \\ \\ -15x+8x=24-10 \\ \\ -7x=14 \\ \\ x=-2$