# Solve for w 2|3w+8|-13<=-5

Write as a piecewise.

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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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Subtract from both sides of the inequality.

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 the right side.

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Move the negative in front of the fraction.

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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Subtract from both sides of the inequality.

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 the right side.

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Move the negative in front of the fraction.

In the piece where is negative, remove the absolute value and multiply by .

Write as a piecewise.

Simplify .

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Simplify each term.

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Apply the distributive property.

Multiply by .

Multiply by .

Subtract from .

Simplify .

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Simplify each term.

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Apply the distributive property.

Multiply by .

Multiply by .

Apply the distributive property.

Multiply by .

Multiply by .

Subtract from .

Solve when .

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Solve for .

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

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Subtract from both sides of the inequality.

Subtract from .

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 the right side.

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Cancel the common factor of and .

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Factor out of .

Cancel the common factors.

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Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Find the intersection of and .

Solve when .

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Solve for .

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

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Add to both sides of the inequality.

Add and .

Divide each term in by and simplify.

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Divide each term in by . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

Simplify the left side.

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Cancel the common factor of .

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Cancel the common factor.

Divide by .

Simplify the right side.

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Divide by .

Find the intersection of and .

Find the union of the solutions.

The result can be shown in multiple forms.

Inequality Form:

Interval Notation:

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