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1. 方程 $ 11 - 3 ( x + 1 ) = 8 $ 的解为______.
答案
x=0
解析
解：$11 - 3(x + 1) = 8$
$11 - 3x - 3 = 8$
$8 - 3x = 8$
$-3x = 0$
$x = 0$
$11 - 3x - 3 = 8$
$8 - 3x = 8$
$-3x = 0$
$x = 0$
2. 方程 $ - \frac { 1 } { 3 } ( x + 5 ) + \frac { 1 } { 3 } = - \frac { 5 } { 3 } $ 的解为______.
答案
x=1
解析
解：方程两边同乘3，得$-(x + 5) + 1 = -5$
去括号，得$-x - 5 + 1 = -5$
合并同类项，得$-x - 4 = -5$
移项，得$-x = -5 + 4$
合并同类项，得$-x = -1$
系数化为1，得$x = 1$
$x=1$
去括号，得$-x - 5 + 1 = -5$
合并同类项，得$-x - 4 = -5$
移项，得$-x = -5 + 4$
合并同类项，得$-x = -1$
系数化为1，得$x = 1$
$x=1$
3. 方程 $ 3 t - 4 ( t - 6 ) = - 21 $ 的解为______.
答案
t=45
解析
解：$3t - 4(t - 6) = -21$
$3t - 4t + 24 = -21$
$-t = -45$
$t = 45$
$3t - 4t + 24 = -21$
$-t = -45$
$t = 45$
4. 方程 $ - 6 ( m - 1 ) + 2 m = 13 $ 的解为______.
答案
$m=-\frac{7}{4}$
解析
解：$-6(m - 1) + 2m = 13$
$-6m + 6 + 2m = 13$
$-4m = 7$
$m=-\frac{7}{4}$
$-6m + 6 + 2m = 13$
$-4m = 7$
$m=-\frac{7}{4}$
5. 方程 $ 0.2 ( x - 2 ) - 0.4 = - 0.6 x $ 的解为______.
答案
x=1
解析
解：$0.2(x - 2) - 0.4 = -0.6x$
$0.2x - 0.4 - 0.4 = -0.6x$
$0.2x - 0.8 = -0.6x$
$0.2x + 0.6x = 0.8$
$0.8x = 0.8$
$x = 1$
$x=1$
$0.2x - 0.4 - 0.4 = -0.6x$
$0.2x - 0.8 = -0.6x$
$0.2x + 0.6x = 0.8$
$0.8x = 0.8$
$x = 1$
$x=1$
6. 方程 $ - 4 - \frac { 3 } { 10 } ( y + 3 ) = 0.2 y $ 的解为______.
答案
$y=-\frac{49}{5}$
解析
解：$-4 - \frac{3}{10}(y + 3) = 0.2y$
$-4 - \frac{3}{10}y - \frac{9}{10} = \frac{1}{5}y$
$-\frac{49}{10} = \frac{1}{5}y + \frac{3}{10}y$
$-\frac{49}{10} = \frac{1}{2}y$
$y = -\frac{49}{5}$
$-4 - \frac{3}{10}y - \frac{9}{10} = \frac{1}{5}y$
$-\frac{49}{10} = \frac{1}{5}y + \frac{3}{10}y$
$-\frac{49}{10} = \frac{1}{2}y$
$y = -\frac{49}{5}$
7. $ x - 3 ( 1 - x ) = - 2 $
答案
$x=\frac{1}{4}$
解析
解：$x - 3 + 3x = -2$
$4x - 3 = -2$
$4x = 1$
$x = \frac{1}{4}$
$4x - 3 = -2$
$4x = 1$
$x = \frac{1}{4}$
8. $ 3 - ( 1 + 2 x ) = 2 x $
答案
$x=\frac{1}{2}$
解析
$3-(1+2x)=2x$
$3-1-2x=2x$
$2-2x=2x$
$-2x-2x=-2$
$-4x=-2$
$x=\frac{1}{2}$
$3-1-2x=2x$
$2-2x=2x$
$-2x-2x=-2$
$-4x=-2$
$x=\frac{1}{2}$
9. $ 7 ( 2 x - 1 ) - 3 ( 4 x - 1 ) = 4 $
答案
x=4
解析
解：$7(2x - 1) - 3(4x - 1) = 4$
$14x - 7 - 12x + 3 = 4$
$2x - 4 = 4$
$2x = 8$
$x = 4$
$14x - 7 - 12x + 3 = 4$
$2x - 4 = 4$
$2x = 8$
$x = 4$
10. $ 2 ( 4 a - 2 ) - 6 = 3 ( 4 a - 2 ) $
答案
a=-1
解析
解：$2(4a - 2) - 6 = 3(4a - 2)$
$8a - 4 - 6 = 12a - 6$
$8a - 10 = 12a - 6$
$8a - 12a = -6 + 10$
$-4a = 4$
$a = -1$
$8a - 4 - 6 = 12a - 6$
$8a - 10 = 12a - 6$
$8a - 12a = -6 + 10$
$-4a = 4$
$a = -1$
11. $ ( 3 x - 1 ) - 3 ( 2 x - 5 ) - ( x + 3 ) + 9 = 0 $
答案
x=5
解析
解：$(3x - 1) - 3(2x - 5) - (x + 3) + 9 = 0$
$3x - 1 - 6x + 15 - x - 3 + 9 = 0$
$(3x - 6x - x) + (-1 + 15 - 3 + 9) = 0$
$-4x + 20 = 0$
$-4x = -20$
$x = 5$
$3x - 1 - 6x + 15 - x - 3 + 9 = 0$
$(3x - 6x - x) + (-1 + 15 - 3 + 9) = 0$
$-4x + 20 = 0$
$-4x = -20$
$x = 5$
13. $ 4 x - 3 ( 21 - x ) = 6 x - 7 ( 9 - x ) $
答案
x=0
解析
解：$4x - 3(21 - x) = 6x - 7(9 - x)$
$4x - 63 + 3x = 6x - 63 + 7x$
$7x - 63 = 13x - 63$
$7x - 13x = -63 + 63$
$-6x = 0$
$x = 0$
$4x - 63 + 3x = 6x - 63 + 7x$
$7x - 63 = 13x - 63$
$7x - 13x = -63 + 63$
$-6x = 0$
$x = 0$
14. $ 2 ( x + 2 ) + 3 ( 3 x - 1 ) = \frac { 1 } { 5 } ( 1 - x ) $
答案
$x=-\frac{1}{14}$
解析
解：$2(x + 2) + 3(3x - 1) = \frac{1}{5}(1 - x)$
$2x + 4 + 9x - 3 = \frac{1}{5} - \frac{1}{5}x$
$11x + 1 = \frac{1}{5} - \frac{1}{5}x$
$55x + 5 = 1 - x$
$56x = -4$
$x = -\frac{1}{14}$
$2x + 4 + 9x - 3 = \frac{1}{5} - \frac{1}{5}x$
$11x + 1 = \frac{1}{5} - \frac{1}{5}x$
$55x + 5 = 1 - x$
$56x = -4$
$x = -\frac{1}{14}$
13. $ 4 x - 3 ( 21 - x ) = 6 x - 7 ( 9 - x ) $ 14. $ 2 ( x + 2 ) + 3 ( 3 x - 1 ) = \frac { 1 } { 5 } ( 1 - x ) $
答案
【解析】：
题目考查的是一元一次方程的解法，特别是去括号的步骤。
对于形如$a(b+c)$的表达式，需要将其展开为$ab+ac$。
然后，将方程两边的同类项进行合并，从而解出x的值。
【答案】：
解：
13. $4x - 3(21 - x) = 6x - 7(9 - x)$
去括号：
$4x - 63 + 3x = 6x - 63 + 7x$
移项并合并同类项：
$-6x = -63+63$
$-6x = 0$
得到：
$x = 0$
14. $2(x + 2) + 3(3x - 1) = \frac{1}{5}(1 - x)$
去括号：
$2x + 4 + 9x - 3 = \frac{1}{5} - \frac{1}{5}x$
移项并合并同类项：
$2x + 9x + \frac{1}{5}x = \frac{1}{5} - 4 + 3$
$11x + \frac{1}{5}x = -\frac{4}{5}$
$\frac{56}{5}x = -\frac{4}{5}$
系数化为1得：
$x = -\frac{1}{14}$
题目考查的是一元一次方程的解法，特别是去括号的步骤。
对于形如$a(b+c)$的表达式，需要将其展开为$ab+ac$。
然后，将方程两边的同类项进行合并，从而解出x的值。
【答案】：
解：
13. $4x - 3(21 - x) = 6x - 7(9 - x)$
去括号：
$4x - 63 + 3x = 6x - 63 + 7x$
移项并合并同类项：
$-6x = -63+63$
$-6x = 0$
得到：
$x = 0$
14. $2(x + 2) + 3(3x - 1) = \frac{1}{5}(1 - x)$
去括号：
$2x + 4 + 9x - 3 = \frac{1}{5} - \frac{1}{5}x$
移项并合并同类项：
$2x + 9x + \frac{1}{5}x = \frac{1}{5} - 4 + 3$
$11x + \frac{1}{5}x = -\frac{4}{5}$
$\frac{56}{5}x = -\frac{4}{5}$
系数化为1得：
$x = -\frac{1}{14}$
