I am having a hard time finding the answer for $$ \vert x+2 \rvert \le 6 $$ The answer has to be interval notation and the book says $$ 4 \le x \le 8 $$
There are examples in the book, and I found a rule on Khan Academy to solve absolute value inequalities. The rule is $$ \lvert f(x) \rvert \lt a $$ $$-a \lt f(x) \lt a $$ If I follow it this is how I solve the problem.
The original equation is $ \lvert x+2 \rvert \le 6$
Then I start to solve... $-6 \le x+2 $ and $6 \ge x+2$
The next step for me is $ -8 \le x \le 4 $
This is where I am stuck. I can not find away to find the book's answer. It must be a reflection about the y axis that I am missing? Why is it 8 and not -8?
The answer you found on your own is correct. The book is wrong in this case; must be a printing error. The way you solved it is one of the correct ways to solve it analytically.