Question

Which graph represents the solutions to the inequality |2x − 6| less than or equal to 10?

Answer 1

Answer: Choice A

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Explanation:

The rule I'm going to use is if |x| <= k, then -k <= x <= k
where k is some positive number
The notation <= means "less than or equal to"

|2x-6| <= 10
-10 <= 2x-6 <= 10 ... use the rule mentioned above
-10+6 <= 2x-6+6 <= 10+6 ... add 6 to all sides
-4 <= 2x <= 16
-4/2 <= 2x/2 <= 16/2 ... divide all sides by 2
-2 <= x <= 8

So we'll have a number line with closed circles at -2 and 8. The shaded region is between the closed circles. 
This is a shorthand way of saying what choice A is saying. For some reason, your teacher decided to make the wording more clunky.
Saying "shading to the right of -2 and shading to the left of 8" is the same as "shading between -2 and 8"
So that's why choice A is the answer

Note: the closed circle indicates we include the endpoint as part of the solution set, or shaded region.