[-8, 2]

                         is interval notation for

                             -8 ≦ x ≦ 2

                   and is represented graphically as

--------------⚫======================================⚫------------
-11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5

The midpoint of that interval is found by averaging the endpoints ==-3

Add the opposite of -3, which is +3, to all three sides:

                      -8 + 3 ≦ x + 3 ≦ 2 + 3 

                          -5 ≦ x + 3 ≦ 5

                     That is equivalent to 

                            |x + 3| ≦ 5   

Edwin