3. Решение уравнений со скобками

1) $4(x - 6) = x - 9 \implies 4x - 24 = x - 9 \implies 3x = 15 \implies x = 5$ 2) $6 - 3(x + 1) = 7 - x \implies 6 - 3x - 3 = 7 - x \implies 3 - 3x = 7 - x \implies -2x = 4 \implies x = -2$ 3) $(8x + 3) - (10x + 6) = 9 \implies 8x + 3 - 10x - 6 = 9 \implies -2x - 3 = 9 \implies -2x = 12 \implies x = -6$ 4) $14x - 14 = 7(2x - 3) + 7 \implies 14x - 14 = 14x - 21 + 7 \implies 14x - 14 = 14x - 14$. Это тождество, верное при любом $x$. 5) $3(x - 2) = x + 2 \implies 3x - 6 = x + 2 \implies 2x = 8 \implies x = 4$ 6) $5 - 2(x - 1) = 4 - x \implies 5 - 2x + 2 = 4 - x \implies 7 - 2x = 4 - x \implies -x = -3 \implies x = 3$ 7) $(7x + 1) - (9x + 3) = 5 \implies 7x + 1 - 9x - 3 = 5 \implies -2x - 2 = 5 \implies -2x = 7 \implies x = -3,5$ 8) $3,4 + 2y = 7(y - 2,3) \implies 3,4 + 2y = 7y - 16,1 \implies -5y = -19,5 \implies y = 3,9$ 9) $4(5x + 2) = 10(3x - 3) + 15 \implies 20x + 8 = 30x - 30 + 15 \implies 20x + 8 = 30x - 15 \implies -10x = -23 \implies x = 2,3$ 10) $2(7x - 7) = 7(2x - 3) + 7 \implies 14x - 14 = 14x - 21 + 7 \implies 14x - 14 = 14x - 14$. Это тождество, верное при любом $x$. 11) $5,6 - 3(2 - 0,4x) = 0,4(4x - 1) \implies 5,6 - 6 + 1,2x = 1,6x - 0,4 \implies -0,4 + 1,2x = 1,6x - 0,4 \implies -0,4x = 0 \implies x = 0$ 12) $5(x - 12) = 6(x - 10) - x \implies 5x - 60 = 6x - 60 - x \implies 5x - 60 = 5x - 60$. Это тождество, верное при любом $x$. 13) $0,3(8 - 3y) = 3,2 - 0,8(y - 7) \implies 2,4 - 0,9y = 3,2 - 0,8y + 5,6 \implies 2,4 - 0,9y = 8,8 - 0,8y \implies -0,1y = 6,4 \implies y = -64$ 14) $4(x - 1) = 2(2x - 8) + 12 \implies 4x - 4 = 4x - 16 + 12 \implies 4x - 4 = 4x - 4$. Это тождество, верное при любом $x$. 15) $8(5 - 3x) = 6(2 - 4x) + 7 \implies 40 - 24x = 12 - 24x + 7 \implies 40 = 19$. Корней нет. 16) $7(4x - 1) = 6 - 2(3 - 14x) \implies 28x - 7 = 6 - 6 + 28x \implies 28x - 7 = 28x \implies -7 = 0$. Корней нет. 17) $4 - 6(x + 2) = 3 - 5x \implies 4 - 6x - 12 = 3 - 5x \implies -6x - 8 = 3 - 5x \implies -x = 11 \implies x = -11$ 18) $(5x + 8) - (8x + 14) = 9 \implies 5x + 8 - 8x - 14 = 9 \implies -3x - 6 = 9 \implies -3x = 15 \implies x = -5$ 19) $-7(x + 3) + 9 = 5 - 6x \implies -7x - 21 + 9 = 5 - 6x \implies -7x - 12 = 5 - 6x \implies -x = 17 \implies x = -17$ 20) $-(11x - 7) + (7x + 9) = 8 \implies -11x + 7 + 7x + 9 = 8 \implies -4x + 16 = 8 \implies -4x = -8 \implies x = 2$