Which solution to the equation 1x + 1 + 2 + 2x + 2 is extraneous?

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Understanding the Equation

To identify which solution of the equation 1x + 1 + 2 + 2x + 2 = 0 is extraneous, we first need to simplify and solve the equation.

Simplifying the Equation

We can rearrange the terms:

  • 1x + 2x + 1 + 2 = 0
  • This simplifies to 3x + 3 = 0

Now, we can solve for x:

  • 3x + 3 = 0
  • 3x = -3
  • x = -1

Checking for Extraneous Solutions

Now that we have found the solution, we need to check if it’s extraneous. An extraneous solution is one that does not satisfy the original equation. To do this, we substitute x = -1 back into the original equation:

  • 1(-1) + 1 + 2 + 2(-1) + 2 = 0
  • -1 + 1 + 2 – 2 + 2 = 0
  • 0 = 0

Since the left-hand side equals the right-hand side, x = -1 is a valid solution.

Conclusion

After checking, we see that x = -1 is not extraneous. If there were other solutions found while solving the equation, we would need to check each of them in the original equation to identify if they were extraneous. In this case, since we only have one solution, it stands.

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