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9. 已知关于$x的两个方程\frac {5x+2}{6}= -3和4x-3(a-x)= 6x-7(a-x)$有相同的解,则$a$的值是______.
答案
-6
解析
解方程$\frac{5x + 2}{6}=-3$，两边同乘6得$5x + 2=-18$，移项得$5x=-20$，解得$x=-4$。
将$x = -4$代入$4x-3(a - x)=6x-7(a - x)$，得$4×(-4)-3(a - (-4))=6×(-4)-7(a - (-4))$，即$-16-3(a + 4)=-24-7(a + 4)$。
移项得$-3(a + 4)+7(a + 4)=-24 + 16$，合并同类项得$4(a + 4)=-8$，两边同除以4得$a + 4=-2$，解得$a=-6$。
$-6$
将$x = -4$代入$4x-3(a - x)=6x-7(a - x)$，得$4×(-4)-3(a - (-4))=6×(-4)-7(a - (-4))$，即$-16-3(a + 4)=-24-7(a + 4)$。
移项得$-3(a + 4)+7(a + 4)=-24 + 16$，合并同类项得$4(a + 4)=-8$，两边同除以4得$a + 4=-2$，解得$a=-6$。
$-6$
10. 小华同学在解方程$5x-1= $( )$x+11$时,把“( )”处的数看成了它的相反数,解得$x= 2$,则该方程的正确解为______.
答案
x=3
解析
设“( )”处的数为$a$，小华把它看成了$-a$。
将$x = 2$代入$5x - 1 = -a x + 11$，得：
$5×2 - 1 = -a×2 + 11$
$10 - 1 = -2a + 11$
$9 = -2a + 11$
$-2a = 9 - 11$
$-2a = -2$
$a = 1$
所以原方程为$5x - 1 = 1x + 11$
$5x - x = 11 + 1$
$4x = 12$
$x = 3$
$x=3$
将$x = 2$代入$5x - 1 = -a x + 11$，得：
$5×2 - 1 = -a×2 + 11$
$10 - 1 = -2a + 11$
$9 = -2a + 11$
$-2a = 9 - 11$
$-2a = -2$
$a = 1$
所以原方程为$5x - 1 = 1x + 11$
$5x - x = 11 + 1$
$4x = 12$
$x = 3$
$x=3$
11. (16分)计算:
(1)$-54×2\frac {1}{4}÷(-4\frac {1}{2})×\frac {2}{9}$
(2)$(-3)^{2}-(\frac {3}{2})^{2}×\frac {2}{9}+6÷|-\frac {2}{3}|^{3}$
(1)$-54×2\frac {1}{4}÷(-4\frac {1}{2})×\frac {2}{9}$
(2)$(-3)^{2}-(\frac {3}{2})^{2}×\frac {2}{9}+6÷|-\frac {2}{3}|^{3}$
答案
（1）6 （2）$\frac{115}{4}$
解析
(1) $-54 × 2\frac{1}{4} ÷ (-4\frac{1}{2}) × \frac{2}{9}$
$=-54 × \frac{9}{4} ÷ (-\frac{9}{2}) × \frac{2}{9}$
$=-54 × \frac{9}{4} × (-\frac{2}{9}) × \frac{2}{9}$
$=-54 × (-\frac{2}{9}) × \frac{9}{4} × \frac{2}{9}$
$=12 × \frac{1}{2}$
$=6$
(2) $(-3)^{2} - (\frac{3}{2})^{2} × \frac{2}{9} + 6 ÷ |-\frac{2}{3}|^{3}$
$=9 - \frac{9}{4} × \frac{2}{9} + 6 ÷ (\frac{8}{27})$
$=9 - \frac{1}{2} + 6 × \frac{27}{8}$
$=9 - \frac{1}{2} + \frac{81}{4}$
$=\frac{36}{4} - \frac{2}{4} + \frac{81}{4}$
$=\frac{115}{4}$
12. (32分)解下列方程:
(1)$2x-3(2-x)= 3x+5(2+2x)$
(2)$4-\frac {x-1}{3}= \frac {7-x}{2}$
(3)$\frac {x+2}{4}-\frac {2x-1}{12}= \frac {1}{3}x+1$
(4)$\frac {2x}{0.03}+\frac {0.25-0.1x}{0.02}= \frac {1}{6}$
(1)$2x-3(2-x)= 3x+5(2+2x)$
(2)$4-\frac {x-1}{3}= \frac {7-x}{2}$
(3)$\frac {x+2}{4}-\frac {2x-1}{12}= \frac {1}{3}x+1$
(4)$\frac {2x}{0.03}+\frac {0.25-0.1x}{0.02}= \frac {1}{6}$
答案
（1）x=-2（2）x=-5 （3）x=-$\frac{5}{3}$ （4）x=-0.2
解析
(1)解：$2x - 3(2 - x) = 3x + 5(2 + 2x)$
$2x - 6 + 3x = 3x + 10 + 10x$
$5x - 6 = 13x + 10$
$5x - 13x = 10 + 6$
$-8x = 16$
$x = -2$
(2)解：$4 - \frac{x - 1}{3} = \frac{7 - x}{2}$
$24 - 2(x - 1) = 3(7 - x)$
$24 - 2x + 2 = 21 - 3x$
$-2x + 26 = 21 - 3x$
$-2x + 3x = 21 - 26$
$x = -5$
(3)解：$\frac{x + 2}{4} - \frac{2x - 1}{12} = \frac{1}{3}x + 1$
$3(x + 2) - (2x - 1) = 4x + 12$
$3x + 6 - 2x + 1 = 4x + 12$
$x + 7 = 4x + 12$
$x - 4x = 12 - 7$
$-3x = 5$
$x = -\frac{5}{3}$
(4)解：$\frac{2x}{0.03} + \frac{0.25 - 0.1x}{0.02} = \frac{1}{6}$
$\frac{200x}{3} + \frac{25 - 10x}{2} = \frac{1}{6}$
$400x + 3(25 - 10x) = 1$
$400x + 75 - 30x = 1$
$370x = 1 - 75$
$370x = -74$
$x = -0.2$
13. (12分)按如图所示的程序进行计算,若经过3次输入,最后输出的数是10,求最初输入的数.
答案
设最初输入的数为x,则第2次输入的数为4x-6,第3次输入的数为4(4x-6)-6.由题图可知,4[4(4x-6)-6]-6=10,去括号、移项、合并同类项,得64x=136.系数化为1,得x=$\frac{17}{8}$.所以最初输入的数是$\frac{17}{8}$
