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).
