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# 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.
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: