Question

Решите уравнение 3/4*(5/6-2/3x)=5x-4 1/2

Answer 1

Решите уравнение
3/4*(5/6-2/3x)=5x-4 1/2;

3/4• 5/6 - 2/3х• 3/4= 5х- (2•4+1)/2;

1/4• 5/2 - 1/1х• 1/2= 5х- 9/2;

5/8 - 1/2х + 9/2= 5х;

5/8+ 9/2= 5х +1/2х;

5/8 +(9•4)/(2•4)= 5 1/2х;

5/8+ 36/8= (5•2+1)/2Х;

41/8= 11/2х;

Х= 41/8: 11/2;

Х= 41/8• 2/11;

Х= 41/4• 1/11;

Х=41/44

{Сократили 3/4 и 5/6 наискось 3 и 6 на 3; 2/3х и 3/4, 3 и 3 на 3; 2 и 4 на 2; 41/8 и 2/11, 8 и 2 на 2}.

Проверка
3/4*(5/6-2/3x)=5x-4 1/2;

3/4• (5/6- 2/3• 41/44)= 5/1• 41/44 - (2•4+1)/2;

3/4• (5/6 - 1/3• 41/22)= 205/44 - 9/2;

3/4• (5/6- 41/66)= 205/44 - (9•22)/(2•22);

3/4• ( (5•11)/(6•11) - 41/66) = 205/44 - 198/44;

3/4• (55/66 - 41/66)= 7/44;

3/4• 14/66= 7/44;

1/2• 7/22= 7/44;

7/44= 7/44.
{Сократили 2/3 и 41/44, 2 и 44 на 2; 3/4 и 14/66, на 3 и 66 на 3, 4 и 14 на 2}