Let x be the number

Observe the graph; a dot marked on the graph. So,

the points are included in the solution set.

The numbers are between  and 4.

The solution set is           

All the numbers are between and 4 are greater than 3 units from 1.  

The absolute value of a number is its distance from 0 on the number line.

So, the absolute value inequality for the graph is

Check the solution.

is equivalent to.

Solve the inequality .

                    (Add 1 to both sides)

                                ( Apply Additive invers proparty: )

                                      (Apply Additive invers proparty: )

Solve the inequality .

                (Add 1 to each side)

                            (Apply Additive invers proparty: )

                                 (Subtract: )

The solution set is .Compare the solution

set with solution set derived in step 1. Both the sets are matching. So,

the absolute value inequality for the graph is

The absolute value inequality for the graph is.