What is "which shows the correct solution of the equation?

Understanding "Which Shows the Correct Solution of the Equation"

This concept centers around the fundamental process of solving <a href="https://www.wikiwhat.page/kavramlar/equations" >equations</a> and then verifying if a given solution actually satisfies the original equation.

Here's a breakdown:

• Solving the Equation: The initial step involves applying various algebraic techniques to isolate the variable and find its value. This might include using the <a href="https://www.wikiwhat.page/kavramlar/order%20of%20operations" >order of operations</a>, combining like terms, using the distributive property, or performing inverse operations.

• Potential Solutions: After solving, you arrive at a potential solution (or solutions). This is the value that you believe the variable should be in order for the equation to be true.

• Verification (Checking the Solution): This is the crucial step of substituting the potential solution back into the original equation. If, after substituting, both sides of the equation are equal, then the potential solution is indeed the correct solution. If the two sides are not equal, the potential solution is incorrect.

• Why is this important? Solving equations often involves manipulations that could introduce extraneous solutions. <a href="https://www.wikiwhat.page/kavramlar/extraneous%20solutions" >Extraneous solutions</a> are values that appear to be solutions based on the solving process but don't satisfy the original equation because of steps taken during the solving. Verification is essential to eliminate these.

• Examples: Consider the simple equation x + 2 = 5. Solving gives x = 3. Substituting x = 3 back into the original equation, we get 3 + 2 = 5, which is true. Therefore, x = 3 is the correct solution.

The question "Which shows the correct solution of the equation?" therefore implies the presence of options presenting different solutions and the need to verify each one using the above process to identify the correct answer.