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

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Математика

Галиха

17 мая, 09:37

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

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Ленин · Answer 1

Решите уравнение

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

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

1/4• 5/2 - 1/1 х• 1/2 = 5 х - 9/2;

5/8 - 1/2 х + 9/2 = 5 х;

5/8 + 9/2 = 5 х + 1/2 х;

5/8 + (9•4) / (2•4) = 5 1/2 х;

5/8 + 36/8 = (5•2+1) / 2 Х;

41/8 = 11/2 х;

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; 2/3 х 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}