Question

Act as if parentheses were absolute value lines.

Answer 1

|3x+6|>12

3x+6> 12
x>2

-(3x+6) > 12
-3x-6>12
-3x>18
x<6

Therefore x>2 or x<6

Answer 2

Let's actually write this inequality with the absolute value operator:
|3x+6|-2>10.  The symbol " | " is to be found at the extreme right of the main keyboard; it's the character you get if you type "capital \."

I'd simplify the problem first:   Add 2 to both sides of the inequality.

This results in |3x+6|=8.

Next, I'd factor 3 out of the two terms within the absolute value symbol:

3|x+2|=8, or |x+2|=8/3

One way of solving this is as follows:  Create 2 equations from |x+2|>8/3.  One would be +(x+2)=8/3; the other would be -(x+2)>8/3.

Can you solve these two new inequalities for x?  Your answer to this problem must contain two inequalities for x values.

Another approach would be to regard x = -2 as the center of a circle of radius 8/3.  x would have to be smaller than [-2-8/3] or greater than [-2+8/3].  In words, the distance of x from the center (x=-2) must be greater than 8/3 in either case (remembering that "distance" is always positive).