Answer:
An extraneous solution is a solution that is obtained by solving an equation, but when that solution is substituted back into the original equation, it does not actually satisfy the equation. This usually happens when a certain operation (such as squaring both sides of an equation) introduces additional solutions that do not satisfy the original equation.
Now, let's consider the equation 2x = x. To solve for x, we can subtract x from both sides:
2x - x = x - x
x = 0
So the solution to the equation is x = 0. However, if we substitute x = 0 back into the original equation, we get:
2(0) = 0
Which is true, so x = 0 is a valid solution to the equation. Therefore, there is no extraneous solution in this case.
Explanation: