The number line in the image shows that the distance between x and 2 is 6, so the absolute value equation |x-2|-3=-6$accurately represents this number line.
The absolute value equation that represents the number line in the image is:
|x-2|-3=-6
This equation can be solved by adding 3 to both sides and then taking the absolute value of the resulting expression:
|x-2|=-3+3
|x-2|=0
Since the absolute value of any expression is always non-negative, the only solution to this equation is when x-2 equals 0
x-2=0
x=2
Therefore, the absolute value equation that represents the number line in the image is $|x-2|-3=-6$.
This equation can be interpreted as follows: the distance between x and 2 is equal to 6. This is because the absolute value of an expression represents its distance from zero. In this case, the expression x-2 represents the distance between x and 2, and the absolute value of this expression represents the distance between x and 2 without regard to direction.