小学数学配方法计算20道经典例题详解

例题1：计算 (2x + 3 = 11)

解题思路：首先将方程中的常数项移到等号右边。

解题步骤：

1. (2x + 3 = 11)
2. (2x = 11 - 3)
3. (2x = 8)
4. (x = \frac{8}{2})
5. (x = 4)

答案：(x = 4)

例题2：解方程 (3x - 5 = 14)

解题思路：同样地，先将方程中的常数项移到等号右边。

解题步骤：

1. (3x - 5 = 14)
2. (3x = 14 + 5)
3. (3x = 19)
4. (x = \frac{19}{3})
5. (x \approx 6.33)

答案：(x \approx 6.33)

例题3：计算 (5(x + 2) = 25)

解题思路：先将括号内的表达式乘以括号外的数。

解题步骤：

1. (5(x + 2) = 25)
2. (5x + 10 = 25)
3. (5x = 25 - 10)
4. (5x = 15)
5. (x = \frac{15}{5})
6. (x = 3)

答案：(x = 3)

例题4：解方程 (4(x - 1) = 12)

解题思路：将括号内的表达式乘以括号外的数。

解题步骤：

1. (4(x - 1) = 12)
2. (4x - 4 = 12)
3. (4x = 12 + 4)
4. (4x = 16)
5. (x = \frac{16}{4})
6. (x = 4)

答案：(x = 4)

例题5：计算 (6(x + 3) - 9 = 15)

解题步骤：

1. (6(x + 3) - 9 = 15)
2. (6x + 18 - 9 = 15)
3. (6x + 9 = 15)
4. (6x = 15 - 9)
5. (6x = 6)
6. (x = \frac{6}{6})
7. (x = 1)

答案：(x = 1)

例题6：解方程 (7(x - 2) = 21)

解题步骤：

1. (7(x - 2) = 21)
2. (7x - 14 = 21)
3. (7x = 21 + 14)
4. (7x = 35)
5. (x = \frac{35}{7})
6. (x = 5)

答案：(x = 5)

例题7：计算 (8(x + 4) = 64)

解题步骤：

1. (8(x + 4) = 64)
2. (8x + 32 = 64)
3. (8x = 64 - 32)
4. (8x = 32)
5. (x = \frac{32}{8})
6. (x = 4)

答案：(x = 4)

例题8：解方程 (9(x - 3) = 27)

解题步骤：

1. (9(x - 3) = 27)
2. (9x - 27 = 27)
3. (9x = 27 + 27)
4. (9x = 54)
5. (x = \frac{54}{9})
6. (x = 6)

答案：(x = 6)

例题9：计算 (10(x + 5) - 20 = 30)

解题步骤：

1. (10(x + 5) - 20 = 30)
2. (10x + 50 - 20 = 30)
3. (10x + 30 = 30)
4. (10x = 30 - 30)
5. (10x = 0)
6. (x = \frac{0}{10})
7. (x = 0)

答案：(x = 0)

例题10：解方程 (11(x - 4) = 33)

解题步骤：

1. (11(x - 4) = 33)
2. (11x - 44 = 33)
3. (11x = 33 + 44)
4. (11x = 77)
5. (x = \frac{77}{11})
6. (x = 7)

答案：(x = 7)

例题11：计算 (12(x + 6) = 72)

解题步骤：

1. (12(x + 6) = 72)
2. (12x + 72 = 72)
3. (12x = 72 - 72)
4. (12x = 0)
5. (x = \frac{0}{12})
6. (x = 0)

答案：(x = 0)

例题12：解方程 (13(x - 5) = 65)

解题步骤：

1. (13(x - 5) = 65)
2. (13x - 65 = 65)
3. (13x = 65 + 65)
4. (13x = 130)
5. (x = \frac{130}{13})
6. (x = 10)

答案：(x = 10)

例题13：计算 (14(x + 7) - 28 = 42)

解题步骤：

1. (14(x + 7) - 28 = 42)
2. (14x + 98 - 28 = 42)
3. (14x + 70 = 42)
4. (14x = 42 - 70)
5. (14x = -28)
6. (x = \frac{-28}{14})
7. (x = -2)

答案：(x = -2)

例题14：解方程 (15(x - 6) = 45)

解题步骤：

1. (15(x - 6) = 45)
2. (15x - 90 = 45)
3. (15x = 45 + 90)
4. (15x = 135)
5. (x = \frac{135}{15})
6. (x = 9)

答案：(x = 9)

例题15：计算 (16(x + 8) = 128)

解题步骤：

1. (16(x + 8) = 128)
2. (16x + 128 = 128)
3. (16x = 128 - 128)
4. (16x = 0)
5. (x = \frac{0}{16})
6. (x = 0)

答案：(x = 0)

例题16：解方程 (17(x - 7) = 51)

解题步骤：

1. (17(x - 7) = 51)
2. (17x - 119 = 51)
3. (17x = 51 + 119)
4. (17x = 170)
5. (x = \frac{170}{17})
6. (x = 10)

答案：(x = 10)

例题17：计算 (18(x + 9) - 36 = 54)

解题步骤：

1. (18(x + 9) - 36 = 54)
2. (18x + 162 - 36 = 54)
3. (18x + 126 = 54)
4. (18x = 54 - 126)
5. (18x = -72)
6. (x = \frac{-72}{18})
7. (x = -4)

答案：(x = -4)

例题18：解方程 (19(x - 8) = 57)

解题步骤：

1. (19(x - 8) = 57)
2. (19x - 152 = 57)
3. (19x = 57 + 152)
4. (19x = 209)
5. (x = \frac{209}{19})
6. (x \approx 11.05)

答案：(x \approx 11.05)

例题19：计算 (20(x + 10) = 200)

解题步骤：

1. (20(x + 10) = 200)
2. (20x + 200 = 200)
3. (20x = 200 - 200)
4. (20x = 0)
5. (x = \frac{0}{20})
6. (x = 0)

答案：(x = 0)

例题20：解方程 (21(x - 9) = 105)

解题步骤：

1. (21(x - 9) = 105)
2. (21x - 189 = 105)
3. (21x = 105 + 189)
4. (21x = 294)
5. (x = \frac{294}{21})
6. (x = 14)

答案：(x = 14)

通过以上20道例题，我们了解了配方法在解决一元一次方程中的应用。配方法是一种非常实用的解题技巧，希望同学们能够通过不断的练习，熟练掌握这一方法。