The way we solve inequalities with absolute values is that you take the original equation, and turn it into this:
[tex] -10 < |2x-6| < 10 [/tex]
Now we can get rid of the absolute value and solve:
[tex] -10 < 2x-6 < 10 [/tex]
[tex] -10 + 6<2x-6+6 < 10+6 [/tex]
[tex] -4 < 2x < 16 [/tex]
[tex] -2 < x < 8 [/tex]
So, I got -2 < x < 8, which is obviously not an option. But, since the question asks for the subset, which is just a part of the answer set, the answer is D. Note that -1 < x < 7 falls within -2 < x < 8, and thus, D is the answer.
