How do you solve integers and inequalities like lx+8l less than or equal to 2?

Question

those two lines next to x and 8 are integer marks

Answer 1

Whenever you have an inequality of the form, |x| < k, that means
-k < x < k
Whenever you have an inequality of the form, |x| > k, that means
x > k or x < -k

|x+8| <= 2 is the first case above.
-2 <= x+8 <= 2
Subtract 8 from all sides
-10 <= x <= -6
Answer: [-10,-6]

Answer 2

they are absolut value signs

|x+8|=<2
x+8=<2 or x+8>=-2
x=< -6 or x>=-10
so x has to be smaller than -6 and bigger than -10 in other words:
x is an element of [-10,-6]

Answer 3

ms math says it all