for each of the number lines, write an absolute value equation in the form |x-c|=d, where c and d are some numbers, to satisfy the given solution set.

An absolute value that can represent the solution set is: |x - 2|=4
From the number line, we have the domain of the x values to be:
x = -4 to 6
This means that the least x value is -4, and the largest is 6
The absolute value equation is given as:
|x - c|=d
Assume that d = 4.
So, we have:
|x - c|=4
Assume that c is 2.
So, we have:
|x - 2|=4
When solved, we have:
x = -2 or x = 6
-2 and 6 are within the domain of the number line.
Hence, an absolute value that can represent the solution set is: |x - 2|=4
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