Question

How do you solve and write the following in interval notation: `|x + 8| ≥ 2`?

Answer 1

`x <= -10`
`x >= -6`

Explanation:

`Ix + 8I >= 2`
Solve the inequality in 2 parts:
a. `(x + 8) >= 2`
`x >= 2 - 8 -->`x >= -6# b. -(x + 8) >= 2 #- x - 8 >= 2# #- x > 10`-->`x <= -10#
Solution set expressed by intervals:
(-inf., -10] and [-6, inf.)
Note. The 2 end points are included in the solution set
Graph

=========== -10------------ -6=========== 0===============