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Ответы к стр. 123
Решите уравнение (619-629):
629. а) 3(x + 2) — x = 10; б) 8 = 3(x — 4) — x;
в) 4x + 3(x — 7) = 5; г) 3(x — 1) + x = 2x;
д) 5 — x = 4(x — 3); е) 5(x + 4) + x = 6;
ж) 7 — (2x + 3) = 9; з) 3(x — 7) — 6x = —x;
и) 1/2(x — 4) + 3x = 5; к) 2(x + 3/5) — x = 3 1/5;
л) 5x — (1/2 x + 9) = 18; м) -2(1/3 x + 7) = -21.
а) 3(x + 2) — x = 10,
3x + 6 — x = 10,
(3 — 1)x = 10 — 6,
2x = 4,
x = 4 : 2,
х = 2;
б) 8 = 3(x — 4) — x,
8 = 3x — 12 — x,
8 + 12 = (3 — 1)х,
20 = 2х,
x = 20 : 2,
х = 10;
в) 4x + 3(x — 7) = 5,
4x + 3x — 21 = 5,
(4 + 3)x = 5 + 21,
7x = 26,
x = 26/7,
х = 3 5/7;
г) 3(x — 1) + x = 2x,
3x — 3 + x = 2x,
3x + x — 2x = 3,
(3 + 1 — 2)x = 3
2x = 3,
x = 3/2,
х = 1 1/2;
д) 5 — x = 4(x — 3),
5 — x = 4x — 12,
5 + 12 = x + 4x,
17 = (1 + 4)х,
17 = 5x,
х = 17/5,
x = 3 2/5;
е) 5(x + 4) + x = 6,
5x + 20 + x = 6,
5x + x = 6 — 20,
(5 + 1)x = -14,
6x = -14,
x = -14/6,
х = -2 1/3;
ж) 7 — (2x + 3) = 9,
7 — 2x — 3 = 9,
-2x = 9 — 7 + 3,
-2x = 5,
x = 5/-2,
х = -2 1/2;
з) 3(x — 7) — 6x = —x,
3x — 21 — 6x = —x,
3x — 6x + x = 21,
-2x = 21,
x = 21/-2,
х = -10 1/2;
и) 1/2(x — 4) + 3x = 5,
1/2 x — 2 + 3x = 5,
1/2 x + 3x = 5 + 2,
3 1/2 x = 7,
x = 7 : 3 1/2,
х = 7 • 2/7,
х = 2;
к) 2(x + 3/5) — x = 3 1/5,
2x + 6/5 — x = 3 1/5,
2x — x = 2 6/5 — 6/5,
(2 — 1)х = 2,
х = 2;
л) 5x — (1/2 x + 9) = 18,
5x — 1/2 x — 9 = 18,
5x — 1/2 x = 18 + 9,
(5 — 1/2)х = 27,
4 1/2 x = 27,
x = 27 : 4 1/2,
х = 27 • 2/9,
х = 6;
м) -2(1/3 x + 7) = -21,
— 2/3 x — 14 = -21,
— 2/3 x = -21 + 14,
— 2/3 x = -7,
x = -7 : (- 2/3),
х = -7 • (- 3/2),
х = 21/2,
х = 10 1/2.
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Ответы по математике. 6 класс. Учебник. Никольский С.М., Потапов М.К., Решетников Н.Н., Шевкин А.В.