To find the interval for the first piece, find where the inside of the absolute value is non-negative.

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.

Add to both sides of the inequality.

In the piece where is negative, remove the absolute value and multiply by .

Write as a piecewise.

Simplify .

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 |x-1|<5