如何求解两步线性方程？

两步方程属于代数的父主题，它有助于以数学表达式的形式表示问题。代数是对数学符号和操作符号规则的研究。代数表达式包括常数、变量如x、y、z、a、b等，以及数学运算符如变量之间的加法、减法、乘除法。

两步方程

两步方程是只能通过两步求解的方程。这些方程很容易求解，但与一步方程相比有点复杂。在求解两步方程时，对等号两边进行算术运算。两步方程是可以分两步求解的代数问题。这里变量被隔离在“=”的一侧以找到它的值。两步方程的一般形式是 ax + b = c 其中 a、b、c 是实数。

例子： 2x + 3 = 0, 7a – 5 = 2, (2/3)x + 1 = 4

求解两步方程的步骤

These Two-Step Equations can be solved easily. It needed just one more step extra as compared to solving one-step equations. The variable is isolated on one side of “=” to determine its value. The steps needed are mentioned below,

1. Add or Subtract to isolate the variable.
2. Multiply or Divide to find the value of a variable.

示例问题

问题 1：求解方程 3x + 3 = 12

解决方案：

Given two step equation 3x + 3 = 12

Step 1: Subtract 3 from both sides.

3x + 3 – 3 = 12 – 3

3x = 9

Step 2: Divide the equation with 3 on both sides

(3x/3) = (9/3)

x = 3

This can be verified by substituting x = 3 in the given equation,

3(3) + 3 = 12

9 + 3 = 12

12 = 12

Hence it was proved that on solving the given equation, we got x = 3.

问题 2：求解方程 x – 5 = 2

解决方案：

Given two step equation x – 5 = 2

Step 1: Add 5 to both sides.

x – 5 + 5 = 2 + 5

x = 7

As the coefficient of variable is 1, No need to perform the step 2. The above result can be verified by substituting x = 7 in the given equation.

x – 5 = 2

7 – 5 = 2

2 = 2

Hence it was proved that on solving the given equation, we got x = 7.

问题 3：求解方程 (x/2) – 5 = 5

解决方案：

Given two step equation (x/2) – 5 = 5

Step 1: Add 5 to both sides.

(x/2) – 5 + 5 = 5 + 5

(x/2) = 10

Step 2: Multiply the equation with 2 on both sides,

(2x/2) = 10 × 2

x = 20

This can be verified by substituting x = 20 in the given equation,

(x/2) – 5 = 5

(20/2) – 5 = 5

10 – 5 = 5

5 = 5

Hence it was proved that on solving the given equation, we got x = 20.

问题 4：求解方程 (2x/3) + 6 = 0

解决方案：

Given two step equation (2x/3) + 6 = 0

Step 1: Subtract 6 from both sides.

(2x/3) + 6 – 6 = 0 – 6

(2x/3) = -6

Step 2: Multiply the equation with 3/2 on both sides,

(2x/3) × (3/2) = -6 × (3/2)

(6x/6) = (-18/2)

x = -9

This can be verified by substituting x = -9 in the given equation,

(2x/3) + 6 = 0

(2(-9)/3) + 6 = 0

(-18/3) + 6 = 0

(-18 + 18)/3 = 0

(0/3) = 0

0 = 0

Hence it was proved that on solving the given equation, we got x = -9.

问题 5：求解方程 4a – 2.6 = 1.4

解决方案：

Given two step equation 4a – 2.6 = 1.4

Step 1: Add 2.6 to both sides.

4a – 2.6 + 2.6 = 1.4 + 2.6

4a = 4

Step 2: Divide the equation with 4 on both sides,

(4a/4) = (4/4)

a = 1

This can be verified by substituting a = 1 in the given equation,

4a – 2.6 = 1.4

4(1) = 1.4 + 2.6

4 = 4

Hence it was proved that on solving the given equation, we got a = 1.

问题 6：求解方程 2z + 1.5 = 2.3

解决方案：

Given two step equation 2z + 1.5 = 2.3

Step 1: Subtract 1.5 from both sides.

2z + 1.5 – 1.5 = 2.3 – 1.5

2z = 0.8

Step 2: Divide the equation with 2 on both sides

(2z/2) = (0.8/2)

z = 0.4

This can be verified by substituting z = 0.4 in the given equation,

2z + 1.5 = 2.3

2(0.4) = 2.3 – 1.5

0.8 = 0.8

Hence it was proved that on solving the given equation, we got z = 0.8.

问题 7：求解方程 1.2a – 1.2 = 1.2

解决方案：

Given two step equation 1.2a – 1.2 = 1.2

Step 1: Add 1.2 to both sides.

1.2a – 1.2 + 1.2 = 1.2 + 1.2

1.2a = 2.4

Step 2: Divide the equation with 1.2 on both sides.

(1.2a/1.2) = (2.4/1.2)

a = 2

This can be verified by substituting a = 2 in the given equation,

1.2a – 1.2 = 1.2

1.2(2) – 1.2 = 1.2

2.4 – 1.2 = 1.2

1.2 = 1.2

Hence it was proved that on solving the given equation, we got a = 2.