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Explain what an extraneous solution is. What is the extraneous solution for
2x = x and why? Show your work

User Olha
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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:

User Kirill Ermolov
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