How Do You Know if a Solution is Extraneous?

To determine if a solution is extraneous, you need to substitute it back into the original equation. An extraneous solution is one that does not satisfy the original equation, often arising when manipulating equations, particularly when squaring both sides or adding/subtracting terms.

Here’s how to check:

1. Take your proposed solution and plug it back into the original equation.
2. Evaluate both sides of the equation with this solution.
3. If both sides are equal, the solution is valid. If they are not equal, then it’s extraneous.

For example, if you solved an equation and found a solution of x = 3, substitute x = 3 back into the original equation. If it holds true, x = 3 is a valid solution. If it does not hold true, x = 3 is an extraneous solution.