Задание 1. Найдите корень уравнения. 1) x+3=-9x; 2) -3x-9=2x; 3) 6x+1=-4x; 4) -2x-4=3x; 5) 3x+3=5x; 6) -8x-3=-6x; 7) 7+8x=-2x-5; 8) -5+9x=10x+4; 9) 1-10x=−5x+10; 10) -4-6x=4x-3; 11) 2+3x=-7x-5; 12) -1-3x=2x+1; 13) 4(x-8)=-5; 14) 10(x-9)=7; 15) 5(x+9)=-8; 16) 4(x+1)=9; 17) 10(x+2)=-7; 18) 5(x-6)=2.

Решим каждое уравнение по порядку: 1) $$x + 3 = -9x$$ Перенесем $$-9x$$ влево, а 3 вправо: $$x + 9x = -3$$ $$10x = -3$$ $$x = \frac{-3}{10}$$ $$x = -0.3$$ 2) $$-3x - 9 = 2x$$ Перенесем $$-3x$$ вправо, а 9 влево: $$-9 = 2x + 3x$$ $$-9 = 5x$$ $$x = \frac{-9}{5}$$ $$x = -1.8$$ 3) $$6x + 1 = -4x$$ Перенесем $$-4x$$ влево, а 1 вправо: $$6x + 4x = -1$$ $$10x = -1$$ $$x = \frac{-1}{10}$$ $$x = -0.1$$ 4) $$-2x - 4 = 3x$$ Перенесем $$-2x$$ вправо, а $$-4$$ влево: $$-4 = 3x + 2x$$ $$-4 = 5x$$ $$x = \frac{-4}{5}$$ $$x = -0.8$$ 5) $$3x + 3 = 5x$$ Перенесем $$3x$$ вправо, а $$3$$ влево: $$3 = 5x - 3x$$ $$3 = 2x$$ $$x = \frac{3}{2}$$ $$x = 1.5$$ 6) $$-8x - 3 = -6x$$ Перенесем $$-8x$$ вправо, а $$-3$$ влево: $$-3 = -6x + 8x$$ $$-3 = 2x$$ $$x = \frac{-3}{2}$$ $$x = -1.5$$ 7) $$7 + 8x = -2x - 5$$ Перенесем $$8x$$ вправо, а $$-5$$ влево: $$7 + 5 = -2x - 8x$$ $$12 = -10x$$ $$x = \frac{12}{-10}$$ $$x = -1.2$$ 8) $$-5 + 9x = 10x + 4$$ Перенесем $$9x$$ вправо, а 4 влево: $$-5 - 4 = 10x - 9x$$ $$-9 = x$$ $$x = -9$$ 9) $$1 - 10x = -5x + 10$$ Перенесем $$-10x$$ вправо, а $$10$$ влево: $$1 - 10 = -5x + 10x$$ $$-9 = 5x$$ $$x = \frac{-9}{5}$$ $$x = -1.8$$ 10) $$-4 - 6x = 4x - 3$$ Перенесем $$-6x$$ вправо, а $$-3$$ влево: $$-4 + 3 = 4x + 6x$$ $$-1 = 10x$$ $$x = \frac{-1}{10}$$ $$x = -0.1$$ 11) $$2 + 3x = -7x - 5$$ Перенесем $$3x$$ вправо, а $$-5$$ влево: $$2 + 5 = -7x - 3x$$ $$7 = -10x$$ $$x = \frac{7}{-10}$$ $$x = -0.7$$ 12) $$-1 - 3x = 2x + 1$$ Перенесем $$-3x$$ вправо, а 1 влево: $$-1 - 1 = 2x + 3x$$ $$-2 = 5x$$ $$x = \frac{-2}{5}$$ $$x = -0.4$$ 13) $$4(x - 8) = -5$$ $$4x - 32 = -5$$ $$4x = -5 + 32$$ $$4x = 27$$ $$x = \frac{27}{4}$$ $$x = 6.75$$ 14) $$10(x - 9) = 7$$ $$10x - 90 = 7$$ $$10x = 7 + 90$$ $$10x = 97$$ $$x = \frac{97}{10}$$ $$x = 9.7$$ 15) $$5(x + 9) = -8$$ $$5x + 45 = -8$$ $$5x = -8 - 45$$ $$5x = -53$$ $$x = \frac{-53}{5}$$ $$x = -10.6$$ 16) $$4(x + 1) = 9$$ $$4x + 4 = 9$$ $$4x = 9 - 4$$ $$4x = 5$$ $$x = \frac{5}{4}$$ $$x = 1.25$$ 17) $$10(x + 2) = -7$$ $$10x + 20 = -7$$ $$10x = -7 - 20$$ $$10x = -27$$ $$x = \frac{-27}{10}$$ $$x = -2.7$$ 18) $$5(x - 6) = 2$$ $$5x - 30 = 2$$ $$5x = 2 + 30$$ $$5x = 32$$ $$x = \frac{32}{5}$$ $$x = 6.4$$ **Ответы:** 1) $$x = -0.3$$ 2) $$x = -1.8$$ 3) $$x = -0.1$$ 4) $$x = -0.8$$ 5) $$x = 1.5$$ 6) $$x = -1.5$$ 7) $$x = -1.2$$ 8) $$x = -9$$ 9) $$x = -1.8$$ 10) $$x = -0.1$$ 11) $$x = -0.7$$ 12) $$x = -0.4$$ 13) $$x = 6.75$$ 14) $$x = 9.7$$ 15) $$x = -10.6$$ 16) $$x = 1.25$$ 17) $$x = -2.7$$ 18) $$x = 6.4