Absolute Value Inquality question?

Question

Question: Solve the absolute value inequality. Graph the solution set on the number line. 
| x - 4 | < 0 
my answer is : 4 < x < 4. Is my answer correct? 
But when I plug in the numbers in the number line, do I just use one 4? 
 

Answer 1

The absolute value inequality is |x - 4 | < 0.

The absolute value inequality |x - 4 | < 0 is equivalent to x - 4 > 0 3 or 4 - x < 0.

Solve the inequality 1: x - 4 > 0.

Add 4 to each side.

x - 4 + 4 > 0 + 4

 x > 4.

Solve the inequality 2: 4 - x < 0.

Subtract 4 from each side.

4 - x - 4 < 0 - 4

- x < - 4

Divide each side by negative 1 and flip symbol.

 - x/-1 > - 4/- 1

Cancel common terms.

x > 4.

The solution set is {x | x > 4 or x < 4}.

So, there is no solutions exist for the given inequality.

Graph the solution set on a number line :

Observe the graph, the open circle means that 4 does not include the solution set.