Short Answer

To solve a linear equation, we follow simple steps to find the value of the variable. First, we simplify the equation if needed, then move all variable terms to one side and constants to the other side. Finally, we isolate the variable by dividing or multiplying.

For example, in 2x + 4 = 10, subtract 4 to get 2x = 6, then divide by 2 to get x = 3. These steps make solving equations easy and clear.

Detailed Explanation:

Steps to Solve Linear Equations

Step 1 Simplify the Equation

The first step is to simplify the given equation. If there are brackets, we remove them by multiplying. If there are like terms, we combine them.

For example:
2(x + 3) = 10
First remove brackets:
2x + 6 = 10

If there are like terms, combine them to make the equation simpler. This step makes further calculations easier.

Step 2 Move Variable Terms

Next, we bring all the variable terms to one side of the equation. Usually, we try to keep variables on the left side.

For example:
x + 5 = 12
We move 5 to the other side by subtracting:
x = 12 − 5

This step helps in separating variables from constants.

Step 3 Move Constants

Now, we move all constant numbers to the other side of the equation. This is done using addition or subtraction.

For example:
2x + 4 = 10
Subtract 4 from both sides:
2x = 6

Now the variable term is separated from constants.

Step 4 Isolate the Variable

In this step, we make the variable stand alone. If the variable is multiplied by a number, we divide both sides by that number.

For example:
2x = 6
Divide both sides by 2:
x = 3

If the variable is divided by a number, we multiply both sides by that number.

Step 5 Check the Solution

After finding the value of the variable, we should check the answer. We do this by putting the value back into the original equation.

For example:
If x = 3 in 2x + 4 = 10
Then: 2(3) + 4 = 6 + 4 = 10

Since both sides are equal, the solution is correct.

Importance of Following Steps

Clear Process

Following steps gives a clear and organized method to solve equations. It avoids confusion and mistakes.

Accurate Results

When steps are followed carefully, the chances of error are reduced, and we get correct answers.

Easy Understanding

Breaking the solution into steps makes it easy for students to understand and learn.

Useful in Complex Problems

These steps are helpful not only for simple equations but also for more complex problems.

Real Life Application

In real life, solving equations step by step helps in handling problems related to money, business, and daily calculations.

Conclusion

Solving linear equations becomes easy when we follow proper steps like simplifying, moving terms, isolating the variable, and checking the answer. These steps help in finding correct solutions and improve problem-solving skills in mathematics and real life.