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

Write as a piecewise.
Click for detailed explanation...
To find the interval for the first piece, find where the inside of the absolute value is non-negative.
Solve the inequality.
Click for detailed explanation...
Subtract from both sides of the inequality.
Divide each term in by and simplify.
Click for detailed explanation...
Divide each term in by .
Simplify the left side.
Click for detailed explanation...
Cancel the common factor of .
Click for detailed explanation...
Cancel the common factor.
Divide by .
Simplify the right side.
Click for detailed explanation...
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.
Click for detailed explanation...
Subtract from both sides of the inequality.
Divide each term in by and simplify.
Click for detailed explanation...
Divide each term in by .
Simplify the left side.
Click for detailed explanation...
Cancel the common factor of .
Click for detailed explanation...
Cancel the common factor.
Divide by .
Simplify the right side.
Click for detailed explanation...
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 .
Click for detailed explanation...
Simplify each term.
Click for detailed explanation...
Apply the distributive property.
Multiply by .
Multiply by .
Subtract from .
Simplify .
Click for detailed explanation...
Simplify each term.
Click for detailed explanation...
Apply the distributive property.
Multiply by .
Multiply by .
Apply the distributive property.
Multiply by .
Multiply by .
Subtract from .
Solve when .
Click for detailed explanation...
Solve for .
Click for detailed explanation...
Move all terms not containing to the right side of the inequality.
Click for detailed explanation...
Subtract from both sides of the inequality.
Subtract from .
Divide each term in by and simplify.
Click for detailed explanation...
Divide each term in by .
Simplify the left side.
Click for detailed explanation...
Cancel the common factor of .
Click for detailed explanation...
Cancel the common factor.
Divide by .
Simplify the right side.
Click for detailed explanation...
Cancel the common factor of and .
Click for detailed explanation...
Factor out of .
Cancel the common factors.
Click for detailed explanation...
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 .
Click for detailed explanation...
Solve for .
Click for detailed explanation...
Move all terms not containing to the right side of the inequality.
Click for detailed explanation...
Add to both sides of the inequality.
Add and .
Divide each term in by and simplify.
Click for detailed explanation...
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.
Click for detailed explanation...
Cancel the common factor of .
Click for detailed explanation...
Cancel the common factor.
Divide by .
Simplify the right side.
Click for detailed explanation...
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: