方程包含两种类型的数量，一种是变量，另一种是数字。但是，为了进行反向操作，我们可以考虑两个等效项。这是学生解决各种问题必须牢记的重要内容之一。同样，对反向操作的充分理解将导致更好的问题解决水平。
在某些问题中，变量将出现在等式的两边。要解决此类问题，我们需要注意以下几点：
- 我们可以在两侧都添加一个带变量的数字，而无需更改方程式或值。
- 我们可以在两侧都减去一个带有变量的数字，而无需更改方程式或值。
- 我们可以在不改变方程式或值的情况下，将一个带有变量的数字两边相乘。
- 我们可以在不改变方程式或值的情况下将带有变量的数字分为两边。
示例：对于x的值，求解14 – 2x = 5x。
步骤1：首先，通过应用一些基本操作，我们需要在一侧分别设置变量并在另一侧设置数字。
Add 2x on both the sides
14 – 2x + 2x = 5x + 2x
(Similarly, we can subtract a term with a variable from both sides of the equation)
步骤2：执行将变量的系数转换为1的操作。
Equation: 14 = 7x
Divide 7 on both the sides
x = 2
示例：求解x的值的64 + 2x = 10x + 8
步骤1：从两侧减去2x：
64 + 2x – 2x = 10x – 2x + 8
64 = 8x + 8
步骤2：从双方减去8：
64 – 8 = 8x + 8 – 8
56 = 8x
步骤3：将两边都除8
x = 7
Note: In every problem of this kind it is always recommended separating the numbers and variables on either side of the equation by applying the reverse operations.
线性方程的样本问题
例子1.解x：35x – 45 = 25
解决方案：
Add 45 to both the sides
35x – 45 + 45 = 25 + 45
35x = 70
Divide 35 on both the sides
x = 2
例子2.解x：22 – 32x = 33 + x
解决方案：
Add 32x on both the sides
22 – 32x + 32x = 33 + x + 32x
22 = 33 + 33x
Subtract 33 from both the sides
22 – 33 = 33 + 33x -33
-11 = 33x
Divide 11 on both the sides
-1 = 3x
Divide 3 on both the sides
x = -1/3
例子3.解x：23x + 4 = 104 + 3x
解决方案：
Subtract 4 from both the sides
23x + 4 – 4 = 104 + 3x – 4
23x = 100 + 3x
Subtract 3x from both the sides
23x – 3x = 100 + 3x – 3x
20x = 100
Divide 20 from both the sides
x = 5
例子4.解x：45x + 21 = 15x + 141
解决方案：
Subtract 21 from both the sides
45x + 21 – 21 = 15x + 141 – 21
45x = 15x + 120
Subtract 15x from both the sides
45x – 15x = 15x + 120 – 15x
30x = 120
Divide 30 on both the sides
x = 4
例子5.解x：28x + 33 = 108 + 3x
解决方案：
Subtract 3x from both the sides
28x + 33 -3x = 108 + 3x – 3x
25x + 33 = 108
Subtract 33 from both the sides
25x + 33 – 33 = 108 – 33
25x = 75
Divide 25 on both the sides
x = 3
例子6.解x：8x + 3x = 34 + 2 + 2x
解决方案：
Simplify: 11x = 36 + 2x
Get the variable on one side:
11x – 2x = 36 + 2x – 2x
9x = 36
Solve using inverse operations:
x = 4
Check Whether: 8(4) + 3(4) = 34 + 2 + 2(4)?
Yes!
示例7.求解y：33y – 32 = 19 – 18y
解决方案：
The equation is already simplified.
Get the variable on one side using inverse operations
33y – 32 + 18y = 19 – 18y + 18y
51y – 32 = 19
51y – 32 + 32 = 19 + 32
51y = 51
y = 1
Check: 33y – 32 = 19 – 18y?
Yes!