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1. 方程$3x - 2 = 4$的解为______.
答案
x=2
解析
解：$3x - 2 = 4$
$3x = 4 + 2$
$3x = 6$
$x = 2$
$3x = 4 + 2$
$3x = 6$
$x = 2$
2. 方程$6 - \frac{1}{2}x = - 4$的解为______.
答案
x=20
解析
解：$6 - \frac{1}{2}x = - 4$
$-\frac{1}{2}x = -4 - 6$
$-\frac{1}{2}x = -10$
$x = (-10) ÷ (-\frac{1}{2})$
$x = 20$
$-\frac{1}{2}x = -4 - 6$
$-\frac{1}{2}x = -10$
$x = (-10) ÷ (-\frac{1}{2})$
$x = 20$
3. 方程$0.2x - 0.1 = 2 - 0.5x$的解为______.
答案
x=3
解析
解：0.2x + 0.5x = 2 + 0.1
0.7x = 2.1
x = 3
0.7x = 2.1
x = 3
4. 方程$- 3x + 5 = - x - 1$的解为______.
答案
x=3
解析
解：$-3x + 5 = -x - 1$
$-3x + x = -1 - 5$
$-2x = -6$
$x = 3$
$-3x + x = -1 - 5$
$-2x = -6$
$x = 3$
5. 方程$\frac{1}{7}x + \frac{1}{14} = - \frac{1}{2}x$的解为______.
答案
$x=-\dfrac{1}{9}$
解析
解：$\frac{1}{7}x + \frac{1}{2}x = -\frac{1}{14}$
$\frac{2}{14}x + \frac{7}{14}x = -\frac{1}{14}$
$\frac{9}{14}x = -\frac{1}{14}$
$x = -\frac{1}{14} × \frac{14}{9}$
$x = -\frac{1}{9}$
$\frac{2}{14}x + \frac{7}{14}x = -\frac{1}{14}$
$\frac{9}{14}x = -\frac{1}{14}$
$x = -\frac{1}{14} × \frac{14}{9}$
$x = -\frac{1}{9}$
6. $x - 7 + 8x = 9x - 3 - 4x$
答案
x=1
解析
解：$x - 7 + 8x = 9x - 3 - 4x$
$9x - 7 = 5x - 3$
$9x - 5x = -3 + 7$
$4x = 4$
$x = 1$
$9x - 7 = 5x - 3$
$9x - 5x = -3 + 7$
$4x = 4$
$x = 1$
7. $56 = 8x + 32 - 2x$
答案
x=4
解析
解：$56=8x+32-2x$
$56=6x+32$
$6x=56-32$
$6x=24$
$x=4$
$56=6x+32$
$6x=56-32$
$6x=24$
$x=4$
8. $\frac{5}{2}x - 7 = \frac{7}{2}x + 1$
答案
x=-8
解析
解：移项，得$\frac{5}{2}x - \frac{7}{2}x = 1 + 7$
合并同类项，得$-x = 8$
系数化为1，得$x = -8$
合并同类项，得$-x = 8$
系数化为1，得$x = -8$
9. $0.7x - 2 - 1.2x = - 2$
答案
x=0
解析
解：$0.7x - 2 - 1.2x = -2$
$-0.5x - 2 = -2$
$-0.5x = 0$
$x = 0$
$-0.5x - 2 = -2$
$-0.5x = 0$
$x = 0$
10. $7.9x + 1.58 + 4x = 7.9x - 8.42$
答案
$x=-\dfrac{5}{2}$
解析
解：$7.9x + 1.58 + 4x = 7.9x - 8.42$
$11.9x + 1.58 = 7.9x - 8.42$
$11.9x - 7.9x = -8.42 - 1.58$
$4x = -10$
$x = -\dfrac{10}{4}$
$x = -\dfrac{5}{2}$
$11.9x + 1.58 = 7.9x - 8.42$
$11.9x - 7.9x = -8.42 - 1.58$
$4x = -10$
$x = -\dfrac{10}{4}$
$x = -\dfrac{5}{2}$
11. $- 4 + \frac{x}{2} = 3x + 1$
答案
x=-2
解析
解：$-4+\frac{x}{2}=3x+1$
移项得：$\frac{x}{2}-3x=1+4$
合并同类项得：$-\frac{5}{2}x=5$
系数化为1得：$x=-2$
移项得：$\frac{x}{2}-3x=1+4$
合并同类项得：$-\frac{5}{2}x=5$
系数化为1得：$x=-2$
12. $- \frac{2}{3}x + 1 + \frac{1}{6}x - 5 = 20$ 13. $\frac{10}{9}z + \frac{2}{7} = \frac{2}{9}z - \frac{5}{7}$
答案
$12. x=-48 13. z=-\dfrac{9}{8}$
解析
12. 解：$-\dfrac{2}{3}x+\dfrac{1}{6}x=20-1+5$
$-\dfrac{4}{6}x+\dfrac{1}{6}x=24$
$-\dfrac{3}{6}x=24$
$-\dfrac{1}{2}x=24$
$x=-48$
13. 解：$\dfrac{10}{9}z-\dfrac{2}{9}z=-\dfrac{5}{7}-\dfrac{2}{7}$
$\dfrac{8}{9}z=-1$
$z=-\dfrac{9}{8}$
$-\dfrac{4}{6}x+\dfrac{1}{6}x=24$
$-\dfrac{3}{6}x=24$
$-\dfrac{1}{2}x=24$
$x=-48$
13. 解：$\dfrac{10}{9}z-\dfrac{2}{9}z=-\dfrac{5}{7}-\dfrac{2}{7}$
$\dfrac{8}{9}z=-1$
$z=-\dfrac{9}{8}$
