# How do you solve and check for extraneous solutions in #abs(x + 6) = 2x#?

Your absolute value equation looks like this

So, you need to check two cases for your equation

The equation becomes

The equation will be

The first solution is valid, since you have

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To solve abs(x + 6) = 2x, first, split the equation into two cases: x + 6 = 2x and -(x + 6) = 2x. Solve each case separately. After solving, check each solution in the original equation to ensure it is valid and not an extraneous solution.

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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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