The absolute value inequality  is graphed below. What is the value of n?

The correct answer is: |x|≥5+n Thus, we can see that no value of n will satisfy the graph.

Hint:
|x| is known as the absolute value of x. It is the non-negative value of x irrespective of its sign. The value of absolute value of x is given by

The symbol |.| is pronounced as ‘modulus’. We read |x| as ‘modulus of x’ or ‘mod x’.
First we find out which inequality represents the graph and then compare it with the given inequality.
Step by step solution:
The given graph is

From the graph, we can observe that the line between -7 and 7 is shaded. The end points are darkened balls and hence are included in the graph.
So the value of x lies between -7 and 7, that is
-7 ≤ x ≤ 7
We can rewrite the above inequality in terms of modulus as follows,
|x| ≤ 7
The given inequality is
5 ≤ |x| - n
Adding n on both sides and rewriting the inequality, we get
|x| ≥ 5 + n
Thus, we can see that no value of n will satisfy the graph.
Note:
If the given inequality was 5 ≥| x| - n, then we would get |x| ≤ 7, which gives the value of n = 7.
Geometrically, |x|  is the positive distance of the point x from the origin on the real line.