**Solving Linear Equations: Inverse Method, Linear Equations in One Variable, Class 8 Math**

**Introduction to Linear Equations:**
A linear equation is an algebraic equation in which the highest power of the variable is 1. It represents a straight line on a graph. Linear equations play a significant role in various fields, including mathematics, physics, economics, and engineering.

**Inverse Method for Solving Linear Equations:**
The inverse method is a systematic approach used to solve linear equations. It involves applying inverse operations to isolate the variable and find its value. The goal is to transform the given equation into the form "variable = value."

**Steps to Solve Linear Equations using the Inverse Method:**

1. **Identify the Variable:** Determine the variable in the equation. In this case, the variable is "x."

Given equation: 2x = 2

2. **Undo Addition or Subtraction:** If there are any addition or subtraction operations involving the variable, undo them by applying the inverse operation. In this case, the equation involves multiplication, so we need to undo it.

Since 2x means 2 multiplied by x, we can undo this multiplication by dividing both sides of the equation by 2.

Dividing both sides by 2, we get: (2x)/2 = 2/2

Simplifying, we have: x = 1

3. **Solution Verification:** After finding the value of the variable, it is essential to verify the solution by substituting it back into the original equation.

Substituting x = 1 into the given equation, we have: 2(1) = 2

Simplifying, we find: 2 = 2

Since the equation is true, the solution x = 1 is correct.

**Conclusion:**
In this example, we solved the linear equation 2x = 2 using the inverse method. By isolating the variable, we found the solution x = 1. It is crucial to verify the solution by substituting it back into the original equation to ensure its accuracy. Linear equations in one variable are fundamental in algebra and are used to solve various real-life problems.

2x = 2 + 8
2x = 10
2x/2 = 10/2 (dividing both sides by 2)
x = 5