# Solve for x |-2+(x-3)|<7 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.
Subtract from .
Add to both sides of the inequality.
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.
Subtract from .
Add to both sides of the inequality.
In the piece where is negative, remove the absolute value and multiply by .
Write as a piecewise.
Subtract from .
Simplify .
Subtract from .
Apply the distributive property.
Multiply by .
Solve when .
Move all terms not containing to the right side of the inequality.
Add to both sides of the inequality.
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 .
Find the intersection of and .
Find the union of the solutions.
The result can be shown in multiple forms.
Inequality Form:
Interval Notation:
Solve for x |-2+(x-3)|<7