Which graph represents the solutions to the inequality |2x − 6| less than or equal to 10? a.) number line with a closed circle on negative 2, shading to the right and a closed circle on 8, shading to the left b.) number line with a closed circle on negative 2, shading to the left and a closed circle on 8, shading to the right c.) number line with an open circle on negative 2, shading to the right and an open circle on 8, shading to the left d.) number line with an open circle on negative 2, shading to the left and an open circle on 8, shading to the right

Choice A



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.