Precalculus Examples

To find the interval for the first piece, find where the inside of the absolute value is non-negative.
Solve the inequality.
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Add to both sides of the inequality.
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Divide by .
In the piece where is non-negative, remove the absolute value.
To find the interval for the second piece, find where the inside of the absolute value is negative.
Solve the inequality.
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Add to both sides of the inequality.
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Divide by .
In the piece where is negative, remove the absolute value and multiply by .
Write as a piecewise.
Simplify .
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Apply the distributive property.
Multiply by .
Multiply by .
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