Short Answer

To verify the solution of an equation, we substitute the value of the variable back into the original equation. If both sides of the equation become equal, then the solution is correct.

For example, if x = 3 is the solution of 2x + 4 = 10, we put 3 in place of x. If both sides give the same result, the answer is verified.

Detailed Explanation:

Verifying the Solution of an Equation

Meaning of Verification

Verification means checking whether the solution we found is correct or not. After solving an equation, it is important to confirm that the value of the variable satisfies the original equation.

This is done by substituting the value of the variable back into the original equation. If both sides of the equation become equal, the solution is correct. If they are not equal, then there is a mistake in solving.

Verification is an important step because it helps in avoiding errors and ensures accuracy.

Steps to Verify a Solution

Step 1 Substitute the Value

First, take the value of the variable that you have found and substitute it into the original equation.

For example, consider the equation:
2x + 4 = 10

If the solution is x = 3, we substitute 3 in place of x:
2(3) + 4

Step 2 Simplify Both Sides

Next, simplify the left-hand side (LHS) and the right-hand side (RHS) of the equation.

LHS = 2 × 3 + 4 = 6 + 4 = 10
RHS = 10

Now, both sides are equal.

Step 3 Compare Both Sides

Finally, compare the LHS and RHS. If they are equal, the solution is correct. If they are not equal, then the solution is wrong and needs to be corrected.

In the example above, LHS = RHS, so the solution x = 3 is correct.

Example of Incorrect Solution

If we take a wrong value, for example x = 2:
LHS = 2(2) + 4 = 4 + 4 = 8
RHS = 10

Since 8 is not equal to 10, this value is not correct.

This shows how verification helps in identifying mistakes.

Importance of Verification

Ensures Accuracy

Verification ensures that the solution is correct. It helps in avoiding wrong answers.

Builds Confidence

When the answer is verified, it gives confidence that the solution is right.

Detects Mistakes

If there is any mistake in solving, verification helps to find it quickly.

Important in Exams

Verification is useful in exams because it helps students check their answers and improve accuracy.

Real Life Application

In real-life calculations, especially in business and finance, verification is important to ensure correct results.

Conclusion

Verifying the solution of an equation is done by substituting the value back into the original equation and checking if both sides are equal. It is an important step that ensures accuracy, detects mistakes, and confirms that the solution is correct.