2025年通城学典初中数学运算能手七年级上册苏科版第60页答案
1. 方程$3(x - 3) - 1 = 8$的解为______.

答案

x=6

解析

解：$3(x - 3) - 1 = 8$
$3x - 9 - 1 = 8$
$3x - 10 = 8$
$3x = 18$
$x = 6$
2. 方程$-11 = 3(x + 5) + 1$的解为______.

答案

x=-9

解析

解：$-11 = 3(x + 5) + 1$
$-11 = 3x + 15 + 1$
$-11 = 3x + 16$
$3x = -11 - 16$
$3x = -27$
$x = -9$
$x=-9$
3. 方程$2x - 4(x + 5) = -5$的解为______.

答案

$x=-\dfrac{15}{2}$

解析

解：$2x - 4(x + 5) = -5$
$2x - 4x - 20 = -5$
$-2x = 15$
$x=-\dfrac{15}{2}$
4. 方程$-0.3(y - 1) = -2.3y$的解为______.

答案

y=-0.15

解析

解：$-0.3(y - 1) = -2.3y$
$-0.3y + 0.3 = -2.3y$
$-0.3y + 2.3y = -0.3$
$2y = -0.3$
$y = -\dfrac{0.3}{2}$
$y = -0.15$
5. 方程$\frac{1}{2}(4x - 1) + 2 = -\frac{7}{2}$的解为______.

答案

$x=-\dfrac{5}{2}$

解析

解：$\frac{1}{2}(4x - 1) + 2 = -\frac{7}{2}$
$2x - \frac{1}{2} + 2 = -\frac{7}{2}$
$2x + \frac{3}{2} = -\frac{7}{2}$
$2x = -\frac{7}{2} - \frac{3}{2}$
$2x = -5$
$x = -\frac{5}{2}$
6. 方程$-\frac{1}{3}(x - 4) + 2x = -1$的解为______.

答案

$x=-\dfrac{7}{5}$

解析

解：$-\frac{1}{3}(x - 4) + 2x = -1$
两边同乘3得：$-(x - 4) + 6x = -3$
去括号得：$-x + 4 + 6x = -3$
合并同类项得：$5x + 4 = -3$
移项得：$5x = -3 - 4$
$5x = -7$
$x = -\frac{7}{5}$
7. $3(x - 5) = x + 1$

答案

x=8

解析

解：3(x - 5) = x + 1
3x - 15 = x + 1
3x - x = 1 + 15
2x = 16
x = 8
8. $4(10 - 0.5x) = -3(x - 2)$

答案

x=-34

解析

解：$4(10 - 0.5x) = -3(x - 2)$
$40 - 2x = -3x + 6$
$-2x + 3x = 6 - 40$
$x = -34$
9. $3(2x + 5) = 2(4x + 3) - 3$

答案

x=6

解析

解：$3(2x + 5) = 2(4x + 3) - 3$
$6x + 15 = 8x + 6 - 3$
$6x + 15 = 8x + 3$
$6x - 8x = 3 - 15$
$-2x = -12$
$x = 6$
10. $4(m + \frac{1}{2}) = 6 - 2(m - 7)$

答案

m=3

解析

解：$4(m + \frac{1}{2}) = 6 - 2(m - 7)$
$4m + 2 = 6 - 2m + 14$
$4m + 2m = 6 + 14 - 2$
$6m = 18$
$m = 3$
11. $5(x - 4) + 2x = 7 - (x - 1)$

答案

$x=\dfrac{7}{2}$

解析

解：$5(x - 4) + 2x = 7 - (x - 1)$
$5x - 20 + 2x = 7 - x + 1$
$7x - 20 = 8 - x$
$7x + x = 8 + 20$
$8x = 28$
$x = \dfrac{28}{8} = \dfrac{7}{2}$
12. $4x - 3(20 - x) = 5x - 7(20 - x)$

答案

x=16

解析

解：$4x - 3(20 - x) = 5x - 7(20 - x)$
$4x - 60 + 3x = 5x - 140 + 7x$
$7x - 60 = 12x - 140$
$-5x = -80$
$x = 16$