# Solve the Absolute Value Inequality for v -3|1-2/3v|=-9

Divide each term in by and simplify.

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Divide each term in by .

Simplify the left side.

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Cancel the common factor of .

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Cancel the common factor.

Divide by .

Simplify each term.

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Combine and .

Move to the left of .

Simplify the right side.

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Divide by .

Remove the absolute value term. This creates a on the right side of the equation because .

The complete solution is the result of both the positive and negative portions of the solution.

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First, use the positive value of the to find the first solution.

Move all terms not containing to the right side of the equation.

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Subtract from both sides of the equation.

Subtract from .

Multiply both sides of the equation by .

Simplify both sides of the equation.

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Simplify the left side.

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Simplify .

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Cancel the common factor of .

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Move the leading negative in into the numerator.

Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

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Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply.

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Multiply by .

Multiply by .

Simplify the right side.

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Cancel the common factor of .

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Move the leading negative in into the numerator.

Cancel the common factor.

Rewrite the expression.

Next, use the negative value of the to find the second solution.

Move all terms not containing to the right side of the equation.

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Subtract from both sides of the equation.

Subtract from .

Multiply both sides of the equation by .

Simplify both sides of the equation.

Click for detailed explanation...

Simplify the left side.

Click for detailed explanation...

Simplify .

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Cancel the common factor of .

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Move the leading negative in into the numerator.

Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Click for detailed explanation...

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply.

Click for detailed explanation...

Multiply by .

Multiply by .

Simplify the right side.

Click for detailed explanation...

Simplify .

Click for detailed explanation...

Cancel the common factor of .

Click for detailed explanation...

Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply by .

The complete solution is the result of both the positive and negative portions of the solution.

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