# Solve for x |4/5x-4|>8

Write as a piecewise.
To find the interval for the first piece, find where the inside of the absolute value is non-negative.
Solve the inequality.
Combine and .
Add to both sides of the inequality.
Multiply both sides of the equation by .
Multiply by .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
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.
Combine and .
Add to both sides of the inequality.
Multiply both sides of the equation by .
Multiply by .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
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.
Combine and .
Simplify .
Combine and .
Apply the distributive property.
Multiply by .
Solve when .
Solve for .
Move all terms not containing to the right side of the inequality.
Add to both sides of the inequality.
Multiply both sides of the equation by .
Multiply by .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
Find the intersection of and .
Solve when .
Solve for .
Move all terms not containing to the right side of the inequality.
Subtract from both sides of the inequality.
Subtract from .
Multiply each term in by
Multiply each term in by . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
Multiply .
Multiply by .
Multiply by .
Multiply by .
Multiply both sides of the equation by .
Multiply by .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
Find the intersection of and .
Find the union of the solutions.
or
The result can be shown in multiple forms.
Inequality Form:
Interval Notation:
Solve for x |4/5x-4|>8