Решите уравнения: а) 4,75 - (х+2 3/8) = 1 1/6 б) 9 5/28 - (7 1/7-х) = 2 4/21

Question

Марк Матвеев

Математика

11 января, 10:12

Решите уравнения: а) 4,75 - (х+2 3/8) = 1 1/6 б) 9 5/28 - (7 1/7-х) = 2 4/21

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Мирон Пономарев · Answer 1

а) 4,75 - (х + 2 3/8) = 1 1/6;

х + 2 3/8 = 4,75 - 1 1/6;

х + 2 3/8 = 475/100 - 7/6;

х + 2 3/8 = 19/4 - 7/6;

х + 2 3/8 = (19 * 3) / (4 * 3) - (7 * 2) / (6 * 2);

х + 2 3/8 = 57/12 - 14/12;

х + 2 3/8 = 43/12;

х = 43/12 - 19/8;

х = (43 * 2) / (12 * 2) - (19 * 3) / (8 * 3);

х = 86/24 - 57/24;

х = 29/24 = 1 5/24.

Проверка:

4,75 - (29/24 + 2 3/8) = 1 1/6;

475/100 - (29/24 + 19/8) = 7/6;

19/4 - ((29/24 + (19 * 3) / (8 * 3)) = 7/6;

19/4 - (29/24 + 57/24) = 7/6;

19/4 - 86/24 = 7/6;

19/4 - 43/12 = 7/6;

(19 * 3) / (4 * 3) - 43/12 = 7/6

57/12 - 43/12 = 7/6;

14/12 = 7/6;

7/6 = 7/6. Решение верно.

б) 9 5/28 - (7 1/7 - х) = 2 4/21;

50/7 - х = 257/28 - 46/21;

50/7 - х = (257 * 21) / (28 * 21) - (46 * 28) / (21 * 28);

50/7 - х = 5397/588 - 1288/588;

50/7 - х = 4109/588;

50/7 - х = 587/84;

х = 50/7 - 587/84;

х = (50 * 12) / (7 * 12) - 587/84;

х = 600/84 - 587/84;

х = 13/84.

Проверка:

9 5/28 - (7 1/7 - 13/84) = 2 4/21;

257/28 - (50/7 - 13/84) = 46/21;

257/28 - ((12 * 50) / (7 * 12) - 13/84) = 46/21;

257/28 - (600/84 - 13/84) = 46/21;

257/28 - 587/84 = 46/21;

(257 * 3) / (28 * 3) - 587/84 = 46/21;

771/84 - 587/84 = 46/21;

184/84 = 46/21;

46/21 = 46/21. Решение верно.