The inequality that is represented by this number line is |3x - 6| ≥ 15. (Option C).
How to determine the inequality represented in the graph?
The inequality represented in the graph is determined by find the solution of the inequality.
From the graph the solution of the inequality is;
x ≤ - 3 or x ≥ 7
Let's consider option C
|3x - 6| ≥ 15
To solve the absolute value equation shown above, we will have two equations;
3x - 6 ≥ 15 ------ (1)
-(3x - 6) ≥ 15 --------- (2)
From equation (1), the value of x is calculated as;
3x ≥ 15 + 6
3x ≥ 21
x ≥ 7
From equation (2), the value of x is calculated as;
-(3x - 6) ≥ 15
-3x + 6 ≥ 15
-3x ≥ 15 - 6
-3x ≥ 9
x ≤ -9/3
x ≤ - 3
So the inequality that is represented by this number line is |3x - 6| ≥ 15.