Пошаговое объяснение:
1) - 3x - 25 = -6x - 7
-3x + 6x = -7 + 25
3x = 18
x = 6
2) 5(3x - 1) - 6 = 4
15x - 5 - 6 = 4
15x = 4 + 5 + 6
15x = 15
x = 1
3) 9x + 2 = 4(5x - 3) - 8
9x + 2 = 20x - 12 -8
9x - 20x = -12 - 8 - 2
-11x = -22
x = 2
4) 4 - 2(6x - 5) = 6(4x + 3)
4 - 12x + 10 = 24x + 18
-12x - 24x = 18 - 4 - 10
-36x = 4
x = - 4/36 = - 1/9
5) 6(3x - 4) - 7(2x + 5) = 2x - 1
18x - 24 - 14x - 35 = 2x - 1
18x - 14x - 2x = -1 + 24 + 35
2x = 58
x = 29
6) 2,3(x - 0,3) + 0,5x = 2,8x
2,3x - 0,69 + 0,5x = 2,8x
2,3x + 0,5x - 2,8x = 0,69
0x = 0,69 ; корней нет.
7) 2(4x + 5) = 7x - 1
8x + 10 = 7x -1
8x - 7x = -1 - 10
x = -11
8) 7x - 12 = 4x + 9(2x - 3)
7x - 12 = 4x + 18x - 27
7x - 4x - 18x = -27+12
-15x = -15
9) 47x - 7(4x - 3) = 4(5x - 2)
47x - 28x + 21 = 20x - 8
47x - 28x -20x = -8 - 21
-x = - 29
10) 7x - 3(3x + 5) = 1 -4(4x - 3)
7x - 9x - 15 = 1 - 16x + 12
7x - 9x + 16x = 1 + 12 + 15
14x = 28
x= 2
11) 8(x - 2) + (3x - 3) = 11x - 19
8x - 16 + 3x - 3 = 11x - 19
8x + 3x - 11x = -19 + 16 + 3
11x - 11x = -19 + 19
0 = 0 ; решением уравнения является любое число.
16 cosx - 11 sinx = 4
Решим методом вс аргумента:
√(16^2 + 11^2) * sin (x - arcsin 11/√(16^2 + 11^2)) = 4
√(377) * sin (x - arcsin 11/√(377)) = 4
sin (x - arcsin 11/√(377)) = 4/√(377)
x - arcsin 11/√(377) = (-1)^n * arcsin 4/√(377) + 2πn (n ∈ Z)
x = (-1)^n * arcsin 4/√(377) + arcsin 11/√(377) + 2πn (n ∈ Z)
11 sin 2x + 6 cos^2x + 6 = 0
22 sinx * cosx + 6 cos^2 x + 6 * 1 = 0
22 sinx * cosx + 6 cos^2 x + 6 (cos^2 x + sin^2 x) = 0
22 sinx * cosx + 6 cos^2 x + 6 cos^2 x + 6 sin^2 x = 0
6 sin^2 x + 22 sinx * cosx + 12 cos^2 x = 0 I сократим на 2
3 sin^2 x + 11 sinx * cosx + 6 cos^2 x = 0 I Поделим на cos^2 x
3 tg^2 x + 11 tgx + 6 = 0
D = 11^2 - 4 * 6 * 3 = 49
1)tg x = (- 11 - 7)/ 6 < - 1, значит значение не подходит
2)tg x = (- 11 + 7)/ 6 = - 4/6 = - 2/3
tg x = - 2/3
x = - arctg 2/3 + πn (n ∈ Z)
Пошаговое объяснение:
1) - 3x - 25 = -6x - 7
-3x + 6x = -7 + 25
3x = 18
x = 6
2) 5(3x - 1) - 6 = 4
15x - 5 - 6 = 4
15x = 4 + 5 + 6
15x = 15
x = 1
3) 9x + 2 = 4(5x - 3) - 8
9x + 2 = 20x - 12 -8
9x - 20x = -12 - 8 - 2
-11x = -22
x = 2
4) 4 - 2(6x - 5) = 6(4x + 3)
4 - 12x + 10 = 24x + 18
-12x - 24x = 18 - 4 - 10
-36x = 4
x = - 4/36 = - 1/9
5) 6(3x - 4) - 7(2x + 5) = 2x - 1
18x - 24 - 14x - 35 = 2x - 1
18x - 14x - 2x = -1 + 24 + 35
2x = 58
x = 29
6) 2,3(x - 0,3) + 0,5x = 2,8x
2,3x - 0,69 + 0,5x = 2,8x
2,3x + 0,5x - 2,8x = 0,69
0x = 0,69 ; корней нет.
7) 2(4x + 5) = 7x - 1
8x + 10 = 7x -1
8x - 7x = -1 - 10
x = -11
8) 7x - 12 = 4x + 9(2x - 3)
7x - 12 = 4x + 18x - 27
7x - 4x - 18x = -27+12
-15x = -15
x = 1
9) 47x - 7(4x - 3) = 4(5x - 2)
47x - 28x + 21 = 20x - 8
47x - 28x -20x = -8 - 21
-x = - 29
x = 29
10) 7x - 3(3x + 5) = 1 -4(4x - 3)
7x - 9x - 15 = 1 - 16x + 12
7x - 9x + 16x = 1 + 12 + 15
14x = 28
x= 2
11) 8(x - 2) + (3x - 3) = 11x - 19
8x - 16 + 3x - 3 = 11x - 19
8x + 3x - 11x = -19 + 16 + 3
11x - 11x = -19 + 19
0 = 0 ; решением уравнения является любое число.