Question

Why is the answer D? Plz explain.

Answer 1

The way we solve inequalities with absolute values is that you take the original equation, and turn it into this:

$-10 < |2x-6| < 10$

Now we can get rid of the absolute value and solve:

$-10 < 2x-6 < 10$

$-10 + 6$

$-4 < 2x < 16$

$-2 < x < 8$

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.