1. 解下列方程:
(1) $ 3x + 17 = 37 - 2x $; (2) $ 9x - 4(x + 2) = 2(3x + 1) $;
(3) $ 5(12 + 5x) - 4 = 8 - (12 + 5x) $; (4) $ \frac{x - 2}{4} - \frac{2x - 1}{6} = 1 $;
(5) $ \frac{3x - 1}{2} - 1 = \frac{5x - 7}{3} $; (6) $ y - \frac{3y - 5}{4} = 1 - \frac{3 - 2y}{2} $;
(7) $ \frac{3}{2}[\frac{2}{3}(\frac{x}{4} - 1) - 2] - x = 2 $; (8) $ \frac{3x + 1}{2} - 2 = \frac{3x - 2}{10} - \frac{2x + 3}{5} $.
(1) $ 3x + 17 = 37 - 2x $; (2) $ 9x - 4(x + 2) = 2(3x + 1) $;
(3) $ 5(12 + 5x) - 4 = 8 - (12 + 5x) $; (4) $ \frac{x - 2}{4} - \frac{2x - 1}{6} = 1 $;
(5) $ \frac{3x - 1}{2} - 1 = \frac{5x - 7}{3} $; (6) $ y - \frac{3y - 5}{4} = 1 - \frac{3 - 2y}{2} $;
(7) $ \frac{3}{2}[\frac{2}{3}(\frac{x}{4} - 1) - 2] - x = 2 $; (8) $ \frac{3x + 1}{2} - 2 = \frac{3x - 2}{10} - \frac{2x + 3}{5} $.
答案：(1) 解：$3x + 2x = 37 - 17$
$5x = 20$
$x = 4$
(2) 解：$9x - 4x - 8 = 6x + 2$
$5x - 8 = 6x + 2$
$5x - 6x = 2 + 8$
$-x = 10$
$x = -10$
(3) 解：$5(12 + 5x) + (12 + 5x) = 8 + 4$
$6(12 + 5x) = 12$
$12 + 5x = 2$
$5x = -10$
$x = -2$
(4) 解：$3(x - 2) - 2(2x - 1) = 12$
$3x - 6 - 4x + 2 = 12$
$-x - 4 = 12$
$-x = 16$
$x = -16$
(5) 解：$3(3x - 1) - 6 = 2(5x - 7)$
$9x - 3 - 6 = 10x - 14$
$9x - 9 = 10x - 14$
$9x - 10x = -14 + 9$
$-x = -5$
$x = 5$
(6) 解：$4y - (3y - 5) = 4 - 2(3 - 2y)$
$4y - 3y + 5 = 4 - 6 + 4y$
$y + 5 = -2 + 4y$
$y - 4y = -2 - 5$
$-3y = -7$
$y = \frac{7}{3}$
(7) 解：$\left(\frac{x}{4} - 1\right) - 3 - x = 2$
$\frac{x}{4} - 1 - 3 - x = 2$
$\frac{x}{4} - x = 2 + 4$
$-\frac{3}{4}x = 6$
$x = -8$
(8) 解：$5(3x + 1) - 20 = 3x - 2 - 2(2x + 3)$
$15x + 5 - 20 = 3x - 2 - 4x - 6$
$15x - 15 = -x - 8$
$15x + x = -8 + 15$
$16x = 7$
$x = \frac{7}{16}$
$5x = 20$
$x = 4$
(2) 解：$9x - 4x - 8 = 6x + 2$
$5x - 8 = 6x + 2$
$5x - 6x = 2 + 8$
$-x = 10$
$x = -10$
(3) 解：$5(12 + 5x) + (12 + 5x) = 8 + 4$
$6(12 + 5x) = 12$
$12 + 5x = 2$
$5x = -10$
$x = -2$
(4) 解：$3(x - 2) - 2(2x - 1) = 12$
$3x - 6 - 4x + 2 = 12$
$-x - 4 = 12$
$-x = 16$
$x = -16$
(5) 解：$3(3x - 1) - 6 = 2(5x - 7)$
$9x - 3 - 6 = 10x - 14$
$9x - 9 = 10x - 14$
$9x - 10x = -14 + 9$
$-x = -5$
$x = 5$
(6) 解：$4y - (3y - 5) = 4 - 2(3 - 2y)$
$4y - 3y + 5 = 4 - 6 + 4y$
$y + 5 = -2 + 4y$
$y - 4y = -2 - 5$
$-3y = -7$
$y = \frac{7}{3}$
(7) 解：$\left(\frac{x}{4} - 1\right) - 3 - x = 2$
$\frac{x}{4} - 1 - 3 - x = 2$
$\frac{x}{4} - x = 2 + 4$
$-\frac{3}{4}x = 6$
$x = -8$
(8) 解：$5(3x + 1) - 20 = 3x - 2 - 2(2x + 3)$
$15x + 5 - 20 = 3x - 2 - 4x - 6$
$15x - 15 = -x - 8$
$15x + x = -8 + 15$
$16x = 7$
$x = \frac{7}{16}$
解析：
(1) 解：$3x + 2x = 37 - 17$
$5x = 20$
$x = 4$
(2) 解：$9x - 4x - 8 = 6x + 2$
$5x - 8 = 6x + 2$
$5x - 6x = 2 + 8$
$-x = 10$
$x = -10$
(3) 解：$5(12 + 5x) + (12 + 5x) = 8 + 4$
$6(12 + 5x) = 12$
$12 + 5x = 2$
$5x = -10$
$x = -2$
(4) 解：$3(x - 2) - 2(2x - 1) = 12$
$3x - 6 - 4x + 2 = 12$
$-x - 4 = 12$
$-x = 16$
$x = -16$
(5) 解：$3(3x - 1) - 6 = 2(5x - 7)$
$9x - 3 - 6 = 10x - 14$
$9x - 9 = 10x - 14$
$9x - 10x = -14 + 9$
$-x = -5$
$x = 5$
(6) 解：$4y - (3y - 5) = 4 - 2(3 - 2y)$
$4y - 3y + 5 = 4 - 6 + 4y$
$y + 5 = -2 + 4y$
$y - 4y = -2 - 5$
$-3y = -7$
$y = \frac{7}{3}$
(7) 解：$\left(\frac{x}{4} - 1\right) - 3 - x = 2$
$\frac{x}{4} - 1 - 3 - x = 2$
$\frac{x}{4} - x = 2 + 4$
$-\frac{3}{4}x = 6$
$x = -8$
(8) 解：$5(3x + 1) - 20 = 3x - 2 - 2(2x + 3)$
$15x + 5 - 20 = 3x - 2 - 4x - 6$
$15x - 15 = -x - 8$
$15x + x = -8 + 15$
$16x = 7$
$x = \frac{7}{16}$
$5x = 20$
$x = 4$
(2) 解：$9x - 4x - 8 = 6x + 2$
$5x - 8 = 6x + 2$
$5x - 6x = 2 + 8$
$-x = 10$
$x = -10$
(3) 解：$5(12 + 5x) + (12 + 5x) = 8 + 4$
$6(12 + 5x) = 12$
$12 + 5x = 2$
$5x = -10$
$x = -2$
(4) 解：$3(x - 2) - 2(2x - 1) = 12$
$3x - 6 - 4x + 2 = 12$
$-x - 4 = 12$
$-x = 16$
$x = -16$
(5) 解：$3(3x - 1) - 6 = 2(5x - 7)$
$9x - 3 - 6 = 10x - 14$
$9x - 9 = 10x - 14$
$9x - 10x = -14 + 9$
$-x = -5$
$x = 5$
(6) 解：$4y - (3y - 5) = 4 - 2(3 - 2y)$
$4y - 3y + 5 = 4 - 6 + 4y$
$y + 5 = -2 + 4y$
$y - 4y = -2 - 5$
$-3y = -7$
$y = \frac{7}{3}$
(7) 解：$\left(\frac{x}{4} - 1\right) - 3 - x = 2$
$\frac{x}{4} - 1 - 3 - x = 2$
$\frac{x}{4} - x = 2 + 4$
$-\frac{3}{4}x = 6$
$x = -8$
(8) 解：$5(3x + 1) - 20 = 3x - 2 - 2(2x + 3)$
$15x + 5 - 20 = 3x - 2 - 4x - 6$
$15x - 15 = -x - 8$
$15x + x = -8 + 15$
$16x = 7$
$x = \frac{7}{16}$
2. 解方程:
(1) $ x - \frac{0.1x - 2}{0.3} = \frac{2 + 3x}{0.6} $; (2) $ \frac{0.4x + 2.1}{0.5} - \frac{0.5 - 0.2x}{0.03} = 0.6 $.
(1) $ x - \frac{0.1x - 2}{0.3} = \frac{2 + 3x}{0.6} $; (2) $ \frac{0.4x + 2.1}{0.5} - \frac{0.5 - 0.2x}{0.03} = 0.6 $.
答案：(1)解：原方程整理得$x-\frac{x-20}{3}=\frac{20+30x}{6}$
两边同乘6得$6x-2(x-20)=20+30x$
去括号得$6x-2x+40=20+30x$
移项得$6x-2x-30x=20-40$
合并同类项得$-26x=-20$
系数化为1得$x=\frac{10}{13}$
(2)解：原方程整理得$\frac{4x+21}{5}-\frac{50-20x}{3}=0.6$
两边同乘15得$3(4x+21)-5(50-20x)=9$
去括号得$12x+63-250+100x=9$
移项得$12x+100x=9-63+250$
合并同类项得$112x=196$
系数化为1得$x=\frac{7}{4}$
两边同乘6得$6x-2(x-20)=20+30x$
去括号得$6x-2x+40=20+30x$
移项得$6x-2x-30x=20-40$
合并同类项得$-26x=-20$
系数化为1得$x=\frac{10}{13}$
(2)解：原方程整理得$\frac{4x+21}{5}-\frac{50-20x}{3}=0.6$
两边同乘15得$3(4x+21)-5(50-20x)=9$
去括号得$12x+63-250+100x=9$
移项得$12x+100x=9-63+250$
合并同类项得$112x=196$
系数化为1得$x=\frac{7}{4}$
解析：
(1)解：原方程整理得$x-\frac{x-20}{3}=\frac{20+30x}{6}$
两边同乘6得$6x-2(x-20)=20+30x$
去括号得$6x-2x+40=20+30x$
移项得$6x-2x-30x=20-40$
合并同类项得$-26x=-20$
系数化为1得$x=\frac{10}{13}$
(2)解：原方程整理得$\frac{4x+21}{5}-\frac{50-20x}{3}=0.6$
两边同乘15得$3(4x+21)-5(50-20x)=9$
去括号得$12x+63-250+100x=9$
移项得$12x+100x=9-63+250$
合并同类项得$112x=196$
系数化为1得$x=\frac{7}{4}$
两边同乘6得$6x-2(x-20)=20+30x$
去括号得$6x-2x+40=20+30x$
移项得$6x-2x-30x=20-40$
合并同类项得$-26x=-20$
系数化为1得$x=\frac{10}{13}$
(2)解：原方程整理得$\frac{4x+21}{5}-\frac{50-20x}{3}=0.6$
两边同乘15得$3(4x+21)-5(50-20x)=9$
去括号得$12x+63-250+100x=9$
移项得$12x+100x=9-63+250$
合并同类项得$112x=196$
系数化为1得$x=\frac{7}{4}$