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 .

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

Add to both sides of the inequality.

Add and .

Find the intersection of and .

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