На полке стояло несколько книг. Когда на нее поставили еще 19 книг, их стало 47. Сколько книг стояло на полке первоначально?

2. Пусть x — количество книг на полке. Тогда x + 19 = 47, откуда x = 47 - 19 = 28. Ответ: 28 книг. 3. а) 4 + 5 + 1/4 = 9 + 1/4 = 9 1/4; б) (1 + 2) + (3/5 + 2/5) = 3 + 5/5 = 3 + 1 = 4; в) 3 - 5/7 = 2 7/7 - 5/7 = 2 2/7; г) 3 11/15. 4. а) (13/17 + 4/17) + (5/16 + 7/16) = 17/17 + 12/16 = 1 + 3/4 = 1 3/4; б) (11/60 + 5/60) + (9/28 + 19/28) = 16/60 + 28/28 = 4/15 + 1 = 1 4/15; в) 29/44 - 7/44 + 1/6 = 22/44 + 1/6 = 1/2 + 1/6 = 3/6 + 1/6 = 4/6 = 2/3; г) (5/8 + 19/36) - 1/36 = 5/8 + 18/36 = 5/8 + 1/2 = 5/8 + 4/8 = 9/8 = 1 1/8; д) 35/68 - (1/68 + 7/22) — условие неполное, требует уточнения скобок; е) 14/39 - (1/12 + 1/39) = 14/39 - 1/39 - 1/12 = 13/39 - 1/12 = 1/3 - 1/12 = 4/12 - 1/12 = 3/12 = 1/4. 5. 6 2/13 - x = 3 3/13; x = 6 2/13 - 3 3/13 = 5 15/13 - 3 3/13 = 2 12/13. Выражение 13x - 2 = 13 * (2 12/13) - 2 = 13 * (38/13) - 2 = 38 - 2 = 36. Ответ: 36. 6. а) 3/7 - (x - 1/8) = 3/4; 3/7 - x + 1/8 = 3/4; -x = 3/4 - 1/8 - 3/7 = 42/56 - 7/56 - 24/56 = 11/56; x = -11/56; б) 5/7 - y = 2/35 + 6/10 = 4/70 + 42/70 = 46/70 = 23/35; y = 5/7 - 23/35 = 25/35 - 23/35 = 2/35; в) 1/12 + x = 3/4 - 5/6 + 23/24 = 18/24 - 20/24 + 23/24 = 21/24 = 7/8; x = 7/8 - 1/12 = 21/24 - 2/24 = 19/24; г) (3x - 4) * 5/7 = 9/14 - 3/7 + 15/28 = 18/28 - 12/28 + 15/28 = 21/28 = 3/4; 3x - 4 = (3/4) / (5/7) = 3/4 * 7/5 = 21/20 = 1 1/20; 3x = 1 1/20 + 4 = 5 1/20; x = (101/20) / 3 = 101/60 = 1 41/60.