Solve and graph the equation :

The correct answer is: Combining the above two solutions, we get -9< x < 9

Step by step solution:
The given inequality is

 
Adding 6 both sides, we have

 
That is

We use the definition of  , which is

For, ,
We have

Multiplying  on both sides, we have

 

Or

For, ,
We have

That is

 
Combining the above two solutions, we get

 
We plot the above inequality on the real line.

The points -9 and 9 are not included in the graph.

The given inequality contains only one variable. So, the graph is plotted on one dimension, which is the real line. Geometrically, the absolute value of a number may be considered as its distance from zero regardless of its direction. The symbol |.| is pronounced as ‘modulus’. We read |x| as ‘modulus of x’ or ‘mod x’.