Математика 6 класс учебник Виленкин, Жохов 2 часть ответы – задача на повторение 36
- Тип: ГДЗ, Решебник.
- Авторы: Виленкин Н.Я., Жихов В.И., Чесноков А.С. и др.
- Часть: 2.
- Год: 2023-2024.
- Серия: Школа России (ФГОС).
- Издательство: Просвещение.
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Проверочная работа
Номер. П.36.
Найдите корень уравнения:
а) 3/7x + 51/2x – 73/4 = 1 – 4/7x + 51/4x; б) 5 – 21/3z + 44/9z = 71/2z – 65/12z + 61/3; в) 4 · (2/7n + 1) + 21/2 = 6 – 1/3 · (6/7n – 3); г) 2 – (11/3p + 1/7) · 21 = 41/4p – 63/8.
Ответ:а) 3/7x + 51/2x – 73/4 = 1 – 4/7x + 51/4x
3/7x + 4/7x + 51/2x – 51/4x = 1 + 73/4
7/7x + 52/4x – 51/4x = 83/4
x + 1/4x = 83/4
5/4x = 35/4
x = 35/4 ∶ 5/4
x = 35/4 · 4/5
x = 7
Проверка:
3/7 · 7 + 51/2 · 7 – 73/4 = 3 + 11/2 · 7 – 73/4 = 3 + 77/2 – 73/4 = 381/2 – 43/4 = 382/4 – 43/4 = 333/4
1 – 4/7 · 7 + 51/4 · 7 = 1 – 4 + 21/4 · 7 = –3 + 147/4 = 363/4 – 3 = 333/4
333/4 = 333/4 – верно.
Ответ: х = 7.
б) 5 – 21/3z + 44/9z = 71/2z – 65/12z + 61/3
–21/3z + 44/9z – 71/2z + 65/12z = 61/3 – 5 = 11/3
–23/9z + 44/9z – 76/12z + 65/12z = 11/3
21/9z – 11/12z = 11/3
24/36z – 13/36z = 11/3
11/36z = 11/3
37/36z = 4/3
z = 4/3 · 36/37
z = 48/37
z = 111/37
Проверка:
5 – 21/3 · 111/37 + 44/9 · 111/37 = 5 – 111/37 · (23/9 – 44/9) = 5 – 111/37 · (–21/9) = 5 + 48/37 · 19/9 = 5 + 16 · 19/37 · 3 = 5 + 304/111 = 5 + 282/111 = 782/111
71/2 · 111/37 – 65/12 · 111/37 + 61/3 = 111/37 · (76/12 – 65/12) + 61/3 = 48/37 · 13/12 + 61/3 = 52/37 + 61/3 = 115/37 + 61/3 = 145/111 + 637/111 = 782/111
782/111 = 782/111 – верно.
Ответ: z = 111/37.
в) 4 · (2/7n + 1) + 21/2 = 6 – 1/3 · (6/7n – 3)
8/7n + 4 + 21/2 = 6 – 2/7n + 1
8/7n + 2/7n = 6 + 1 – 4 – 21/2
10/7n = 1/2
n = 1/2 ∶ 10/7
n = 1/2 · 7/10
n = 7/20
Проверка:
4 · (2/7 · 7/20 + 1) + 21/2 = 4 · (1/10 + 1) + 21/2 = 0,4 + 4 + 2,5 = 6,9
6 – 1/3 · (6/7 · 7/20 – 3) = 6 – 1/3 · (3/10 – 3) = 6 – 1/10 + 1 = 7 – 0,1 = 6,9
6,9 = 6,9 – верно.
Ответ: n = 7/20.
г) 2 – (11/3p + 1/7) · 21 = 41/4p – 63/8
2 – (4/3p + 1/7) · 21 = 41/4p – 63/8
2 – 28p – 3 = 41/4p – 63/8
–28p – 41/4p = –63/8 – 2 + 3
–321/4p = –53/8
–129/4p = –43/8
p = –42/8 : (–129/4)
p = 42/8 · 4/129
p = 1/6
Проверка:
2 – (11/3 · 1/6 + 1/7) · 21 = 2 – (4/3 · 1/6 + 1/7) · 21 = 2 – (2/9 + 1/7) · 21 = 2 - 2/9 · 21 – 1/7 · 21 = 2 – 14/3 – 3 = –1 – 42/3 = –52/3
41/4 · 1/6 – 63/8 = 17/4 · 1/6 – 63/8 = 17/24 – 69/24 = –(533/24 – 17/24) = –516/24 = –52/3
–52/3 = –52/3 – верно.
Ответ: p = 1/6.
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