# How do you solve the equation and identify any extraneous solutions for #abs(x-2)=6x+18#?

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To solve the equation ( |x - 2| = 6x + 18 ) and identify any extraneous solutions:

- Solve the equation ( |x - 2| = 6x + 18 ).
- Split the equation into two cases: a) ( x - 2 = 6x + 18 ) b) ( -(x - 2) = 6x + 18 )
- Solve each case separately.
- Check each solution to see if it satisfies the original equation.
- Identify any solutions that do not satisfy the original equation as extraneous.

The solutions are the intersection of the solutions for both cases.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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