дидактические материалы алгебра 7 класс Л.И. Звавич, Л.В. Кузнецова

Вариант 2

с-9

 

1. 1) a) 3x + 2 = 0;
3x = -2;
х = -2/3;
б) 3 - 5х = 0;
5x = 3;
х = 3/5;
в) 0,6х + 1,8 = 0;
0,6x = -1,8;
х = -3;
г) 7 - 0,7x = 0;
0,7x = 7;
х = 10.
2) a) 8x - 5 = x - 40;
7x = -35;
x = -5
б) 7t + 21 = t - 3;
6t = -24;
t = -4;
в) 9 + 13y = 35 + 26y;
13y = -26; y = -2;
г) 0,3p - 5 = 6 - 0,7p;
0,3p + 0,7p = 6 + 5;
p = 11;
д) 8,31k - 71 = 1,11k + 1;
7,2k = 72;
k = 10;
e) 9c + 2,65 = 36,85 - 9c;
18c = 34,2; с = 1,9;

3) a) 6x + (3x - 2) = 14;
6x + 3x - 2 = 14;
9x = 16;
x = 1 7/9;
6) 8y - (7y - 142) = 51;
8y - 7y + 142 = 51;
y = -91;
в) 5 = -1 - (3 - 9x);
5 = -1 - 3 + 9x;
9x = 9;
x = 1;
г) 9 - (8x - 11) = 12;
9 - 8x + 11 = 12;
8x = 8;
x = 1;
4) a) (6x + 1) - (3 - 2x) = 14;
6x + 1 - 3 + 2x = 14;
8x = 16;
x = 2;
6) (6 - 2x) + 4 = -5x - 3;
6 - 2х + 4 = -5х - 3;
3x = -13;
x = - 4 1/3;
в) 12 = (7x - 9)-(11 - x);
12 = 7x - 9 - 11 + x;
8x = 32;
x = 4;
г) 11x + 103 = 1 + (12x - 31);
11x + 103 = 1 + 12x - 31;
x = 133.

2. 1) 3t + 5 = 5t + 13; 2t = -8; t = -4;
2) 3t + 17 = 2(5t - 5); 3t + 17 = 10t - 10; 7t = 27; t = 27/7 = 3 6/7;
3) 3(3t - 11) = 5t - 17; 9t - 33 = 5t - 17; 4t = 16; t = 4;
4) 11 - 13t = 8t + 11 + 7; 21t = -7; t = -1/3;
5) 0,5t + 3,1 + 8 = 0,5t - 4,9;
0 = -16 - неверно, значит, такого t не существует;
6) 81 - 8,3t - (75 - 8,3t) = 3; 81 - 8,3t - 75 + 8,3t = 3;
6 = 3 - неверно, значит, такого t не существует.

3. a) (10x - 3) + (14x - 4) = 8 - (15 - 22x);
10x - 3 + 14x - 4 = 8 - 15 + 22x; 2x = 0; x = 0;
б) (2х + 3) - (5x + 11) = 7 + (13 - 2x);
2х + 3 - 5x - 11 = 7 + 13 - 2x; x = -28;
в) (7 - 10x) - (8 - 8x) + (10x + 6) = -8;
7 - 10x - 8 + 8x + 10x + 6 = -8; 8x =-13; x = -13/8 = -1 5/8;
г) (2х + 3) + (3x + 4) + (5x + 5) = 12 - 7х;
2x + 3 + 3x + 4 + 5x + 5 = 12 - 7x; 17x = 0; x = 0.

4. 17(3x - 2) = 17(6x + 5) и (3x-2)/19 = (6x+5)/19;
Корень: 3x - 2 = 6x + 5; 3x = -7; x = -7/3 = -2 1/3.

5. 8x + 3 = 8x + 7; 9 - x = 11 - х; |x| + 3 = 0.