Nothing but just you have to solve the equation and check it this is known as trial and error method.

What is meant by an Equation?

An equation is a mathematical statement that asserts the equality of two expressions. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The LHS and RHS may contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

Solving Equations by Trial and Error Method

The trial and error method is one of the simplest and most intuitive methods to solve equations. It involves substituting different values into the equation until a solution is found. Here's how you can solve an equation using the trial and error method:

1. Identify the equation: Start by clearly identifying the equation you need to solve. For example, consider the equation: 3x + 7 = 22.

2. Choose a trial value: Select a value for the variable (x) and substitute it into the equation. It is usually best to start with a simple value, such as x = 0.

3. Evaluate the equation: Substitute the trial value into the equation and evaluate both sides. In our example, if we substitute x = 0, we get: 3(0) + 7 = 22. Simplifying this gives us: 7 = 22.

4. Assess the result: Compare the values on both sides of the equation. If they are equal, then the trial value is a solution. In our example, since 7 does not equal 22, we know that x = 0 is not a solution.

5. Repeat the process: Choose another trial value and substitute it into the equation. Keep repeating steps 3 and 4 until a solution is found. In our example, let's try x = 5: 3(5) + 7 = 22. Simplifying, we get: 22 = 22.

6. Determine the solution: If the trial value makes both sides of the equation equal, then it is the solution. In our example, x = 5 is a solution since 22 does equal 22.

7. Check the solution: Finally, substitute the solution back into the original equation to verify its correctness. In our example, substituting x = 5 into 3x + 7 = 22 gives us: 3(5) + 7 = 22, which simplifies to: 22 = 22. This confirms that x = 5 is indeed the correct solution.

Summary

An equation is a mathematical statement that asserts the equality of two expressions. The trial and error method is a simple and intuitive approach to solving equations. It involves substituting different values into the equation until a solution is found. By evaluating the equation and comparing the values on both sides, you can determine if a trial value is a solution. Repeat the process with different trial values until the equation is satisfied. Finally, check the solution by substituting it back into the original equation.