Рациональные числа
Уравнения
Ответы к стр. 122
618. Является ли число 2 корнем уравнения:
а) x — 2 = 0; б) x + 4 = 0; в) 2x = 4;
г) 3x — 4 = x; д) x + 3 = 2x + 1; е) 3x + 4 = 6x — 2?
Подставим в уравнение вместо х число 2.
а) 2 — 2 = 0,
0 = 0 — является;
б) 2 + 4 = 0,
6 ≠ 0 — не является;
в) 2 • 2 = 4,
4 = 4 — является;
г) 3 • 2 — 4 = 2,
2 = 2 — является;
д) 2 + 3 = 2 • 2 + 1,
5 = 5 — является;
е) 3 • 2 + 4 = 6 • 2 — 2,
10 = 10 — является.
Решите уравнение (619-629):
619. а) х — 2 = 0; б) х + 4 = 0; в) 100 + х = 0; г) х — 5 = 6;
д) х + 2 = 5; е) х — 11 = -7; ж) 12 + х = 17; з) х + 7 = 7.
а) х — 2 = 0,
х = 0 + 2,
х = 2;
б) х + 4 = 0,
х = 0 — 4,
х = -4;
в) 100 + х = 0,
х = 0 — 100,
х = -100;
г) х — 5 = 6,
х = 6 + 5,
х = 11;
д) х + 2 = 5,
х = 5 — 2,
х = 3;
е) х — 11 = -7,
х = -7 + 11,
х = 4;
ж) 12 + х = 17,
х = 17 — 12,
х = 5;
з) х + 7 = 7,
х = 7 — 7,
х = 0.
620. а) 5 + x = 3; б) -7 + x = -2; в) x + 3 = -6;
г) 12 + x = -8; д) x + 18 = 18; е) -13 + x = -5;
ж) x — 1/5 = 2; з) x — 2 = 1/2; и) x — 4 = 1 1/3.
а) 5 + x = 3,
x = 3 — 5,
x = -2;
б) -7 + x = -2,
x = -2 + 7,
x = 5;
в) x + 3 = -6,
x = -6 — 3,
x = -9;
г) 12 + x = -8,
x = -8 — 12,
x = -20;
д) x + 18 = 18,
x = 18 — 18,
x = 0;
е) -13 + x = -5,
x = -5 + 13,
x = 8;
ж) x — 1/5 = 2,
x = 2 + 1/5,
x = 2 1/5;
з) x — 2 = 1/2,
x = 1/2 + 2,
x = 2 1/2;
и) x — 4 = 1 1/3,
x = 1 1/3 + 4,
x = 5 1/3.
621. а) x — 1/2 = 1/2; б) x — 1/3 = 1/4; в) x — 1/18 = 1/12;
г) x — 1 = — 1/3; д) 1/7 + x = 11; е) 1 1/5 + x = 1;
ж) x — 6 1/3 = -3 2/3; з) 7/9 + x = 2 1/2; и) x — 2 1/2 = -1 3/5.
а) x — 1/2 = 1/2,
x = 1/2 + 1/2,
x = 2/2,
х = 1;
б) x — 1/3 = 1/4,
x = 1/4 + 1/3,
x = 3+4/12,
х = 7/12;
в) x — 1/18 = 1/12,
x = 1/12 + 1/18,
x = 3+2/36,
х = 5/36;
г) x — 1 = — 1/3,
x = — 1/3 + 1,
x = 2/3;
д) 1/7 + x = 11,
x = 11 — 1/7,
x = 10 6/7;
е) 1 1/5 + x = 1,
x = 1 — 1 1/5,
x = — 1/5;
ж) x — 6 1/3 = -3 2/3,
x = -3 2/3 + 6 1/3,
x = 2 2/3;
з) 7/9 + x = 2 1/2,
x = 2 1/2 — 7/9,
x = 2 9/18 — 14/18,
х = 1 27/18 — 14/18,
х = 1 13/18;
и) x — 2 1/2 = -1 3/5,
x = -1 3/5 + 2 1/2,
x = -1 6/10 + 2 5/10,
х = 1 15/10 — 1 6/10,
х = 9/10.
622. а) 2x = 4; б) 6x = 24; в) 7x = -14;
г) -5x = 100; д) -2x = -8; е) 12x = -36.
а) 2x = 4,
x = 4 : 2,
х = 2;
б) 6x = 24,
x = 24 : 6,
х = 4;
в) 7x = -14,
x = -14 : 7,
х = -2;
г) -5x = 100,
x = -100 : 5,
х = -20;
д) -2x = -8,
x = -8 : (-2),
х = 4;
е) 12x = -36,
x = -36 : 12,
х = -3.
623. а) 3x = 2; б) 6x = -7; в) -2x = -13; г) 2x = 0;
д) -5x = 0; е) —x = 2; ж) —x = 0; з) —x = -5.
а) 3x = 2,
x = 2/3;
б) 6x = -7,
x = — 7/6,
х = -1 1/6;
в) -2x = -13,
x = -13/-2,
х = 6 1/2;
г) 2x = 0,
x = 0 : 2,
х = 0;
д) -5x = 0,
x = 0 : (-5),
х = 0;
е) —x = 2,
x = 2 : (-1),
х = -2;
ж) —x = 0,
x = 0 : (-1),
х = 0;
з) —x = -5,
x = -5 : (-1),
х = 5.
624. а) 2x = 1/2; б) 3x = — 1/4; в) -2x = 1/4;
г) 1/2 x = 3; д) 3/4 x = 1; е) — 1/3 x = -3;
ж) — 2/7 x = 0; з) -4x = 8/25; и) 2x = 1 1/3.
а) 2x = 1/2,
x = 1/2 : 2,
х = 1/2 • 1/2,
х = 1/4;
б) 3x = — 1/4,
x = — 1/4 : 3,
х = — 1/4 • 1/3,
х = — 1/12;
в) -2x = 1/4,
x = 1/4 : (-2),
х = 1/4 • (- 1/2),
х = — 1/8;
г) 1/2 x = 3,
x = 3 : 12,
х = 3 • 2,
х = 6;
д) 3/4 x = 1,
x = 1 : 3/4,
х = 1 • 4/3,
х = 4/3,
х = 1 1/3;
е) — 1/3 x = -3,
x = -3 : (- 1/3),
х = -3 • (- 3/1),
х = 9/1,
х = 9;
ж) — 2/7 x = 0,
x = 0 : (- 2/7),
х = 0;
з) -4x = 8/25,
x = 8/25 : (-4),
х = 8/25 • (- 1/4),
х = — 2•1/25•1,
х = — 2/25;
и) 2x = 1 1/3,
x = 1 1/3 : 2,
х = 4/3 • 1/2,
х = 2•1/3•1,
х = 2/3.
625. а) 2x — 6 = 0; б) 12 + 3x = 0; в) —x + 7 = 0; г) 15 — 3x = 0;
д) 3x + 1 = 7; е) 5 — 2x = 1; ж) 5x — 2 = 1; з) -5x — 2 = -12.
а) 2x — 6 = 0,
2x = 0 + 6,
х = 6 : 2,
х = 3;
б) 12 + 3x = 0,
3x = 0 — 12,
х = -12 : 3,
х = -4;
в) —x + 7 = 0,
—x = 0 — 7,
х = -7 : (-1),
х = 7;
г) 15 — 3x = 0,
-3x = 0 — 15,
х = -15 : (- 3),
х = 5;
д) 3x + 1 = 7,
3x = 7 — 1,
х = 6 : 3,
х = 2;
е) 5 — 2x = 1,
-2x = 1 — 5,
-2х = -4,
x = -4 : (-2),
х = 2;
ж) 5x — 2 = 1,
5x = 1 + 2,
x = 3/5;
з) -5x — 2 = -12,
-5x = -12 + 2,
х = -10 : (-5),
х = 2.
626. а) 3x + 2x = 10; б) 5x + x = 6; в) 4x + 2x — 7 = 5;
г) 7x + x + 3 = 19; д) 5 = 4x — 3x; е) 8 = 3x — x;
ж) 3x — 1 = 2x; з) 3x — 6 = x.
а) 3x + 2x = 10,
(3 + 2)х = 10,
5x = 10,
x = 10 : 5,
х = 2;
б) 5x + x = 6,
(5 + 1)х = 6,
6x = 6,
x = 6 : 6,
х = 1;
в) 4x + 2x — 7 = 5,
(4 + 2)х = 5 + 7,
6x = 12,
x = 12 : 6,
х = 2;
г) 7x + x + 3 = 19,
(7 + 1)х = 19 — 3,
8x = 16,
x = 16 : 8,
х = 2;
д) 5 = 4x — 3x,
5 = (4 — 3)х,
x = 5;
е) 8 = 3x — x,
8 = (3 — 1)х,
8 = 2x,
x = 8 : 2,
х = 4;
ж) 3x — 1 = 2x,
3x — 2x = 1,
(3 — 2)х = 1,
x = 1;
з) 3x — 6 = x,
3x — x = 6,
(3 — 1)х = 6,
2x = 6,
x = 6 : 2,
х = 3.
627. а) x + 3 = 3x — 7; б) 3 — x = 1 + x; в) 7x + 2 = 3x — 10;
г) 5x — 8 = 3x — 8; д) 1/2 x — 3 = 2 — 1/3 x; е) 5x — 2 1/4 = 1/2 x;
ж) 2/5 x — 1 = 3/4 x — 6; з) 2x — 3/5 = 3/4 x — 1/2.
а) x + 3 = 3x — 7,
3 + 7 = 3x — x,
10 = (3 — 1)х,
10 = 2х,
х = 10 : 2,
х = 5;
б) 3 — x = 1 + x,
3 — 1 = x + x,
2 = (1 + 1)х,
2 = 2х,
х = 2 : 2,
х = 1;
в) 7x + 2 = 3x — 10,
7x — 3x = -10 — 2,
(7 — 3)х = -12,
4x = -12,
x = -12 : 4,
x = -3;
г) 5x — 8 = 3x — 8,
5x — 3x = -8 + 8,
(5 — 3)х = 0,
2х = 0,
х = 0 : 2,
х = 0;
д) 1/2 x — 3 = 2 — 1/3 x,
1/2 x + 1/3 x = 2 + 3,
3/6 x + 2/6 x = 5,
5/6 x = 5,
x = 5 : 5/6,
х = 5 • 6/5,
х = 6;
е) 5x — 2 1/4 = 1/2 x,
5x — 1/2 x = 2 1/4,
(5 — 1/2)х = 2 1/4,
4 1/2 x = 2 1/4,
x = 2 1/4 : 4 1/2,
х = 9/4 • 2/9,
х = 1/2;
ж) 2/5 x — 1 = 3/4 x — 6,
2/5 x — 3/4 x = -6 + 1,
(8/20 — 15/20)х = -5,
— 7/20 х = -5,
х = -5 : (- 7/20),
х = -5 • (- 20/7),
х = 100/7,
х = 14 2/7;
з) 2x — 3/5 = 3/4 x — 1/2,
2x — 3/4 x = — 1/2 + 3/5,
(2 — 3/4)x = — 5/10 + 6/10,
1 1/4 x = 1/10,
х = 1/10 : 5/4,
х = 1/10 • 4/5,
х = 1•2/5•5,
х = 2/25.
628. а) 2(x — 5) = 9; б) 12 + 3(x — 1) = 0; в) -(x + 8) = 3;
г) 1 — 5(2 — 3x) = 6; д) 7 — 3(x + 1) = 6; е) 5 — 2(3 — x) = 11;
ж) 2x — (7 + x) = 2; з) -3 — 3(3 — 2x) = 1.
а) 2(x — 5) = 9,
2x — 10 = 9,
2x = 9 + 10,
x = 19/2,
х = 9 1/2;
б) 12 + 3(x — 1) = 0,
12 + 3x — 3 = 0,
3x = 0 — 12 + 3,
x = -9 : 3,
х = -3;
в) -(x + 8) = 3,
—x — 8 = 3,
—x = 3 + 8,
x = 11 : (-1),
х = -11;
г) 1 — 5(2 — 3x) = 6,
1 — 10 + 15x = 6,
15x = 6 — 1 + 10,
x = 15 : 15,
х = 1;
д) 7 — 3(x + 1) = 6,
7 — 3x — 3 = 6,
-3x = 6 — 7 + 3,
x = 2 : (-3),
х = — 2/3;
е) 5 — 2(3 — x) = 11,
5 — 6 + 2x = 11,
2x = 11 — 5 + 6,
x = 12 : 2,
х = 6;
ж) 2x — (7 + x) = 2,
2x — 7 — x = 2,
(2 — 1)x = 2 + 7,
х = 9;
з) -3 — 3(3 — 2x) = 1,
-3 — 9 + 6x = 1,
6x = 1 + 3 + 9,
x = 13/6,
х = 2 1/6.
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Ответы по математике. 6 класс. Учебник. Никольский С.М., Потапов М.К., Решетников Н.Н., Шевкин А.В.