WEBVTT

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Here is the problem: |x plus 9| equals 10.

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Solve an absolute value equation by splitting it into the cases where the inside is positive or negative.

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Write the problem with the absolute value isolated. The absolute value is already alone on one side, so it can be split into cases.

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Split into two cases. The inside is either c units above zero or c units below zero.

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Solve the positive case.

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Solve the negative case.

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Check each solution in the original equation.

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Write the solution set in interval notation.

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So the answer is x equals negative 19 or x equals 1; interval notation: -19, 1.

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An absolute value measures distance from zero, so |u| equals c means u is exactly c units from zero on either side.

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Substituting negative 19 and 1 gives 10 on the left, matching the right-hand side.