Question

If |x + 2| > 5, then x ______ – 7 or x ______ 3.

Answer 1

If |x + 2| > 5, then x < – 7 or x > 3.

Explanation:

If |x + 2| > 5, then 

x + 2 < – 5 or x + 2 > 5

⇒ x < –5 – 2 or x > 5 – 2

⇒ x < – 7 or x > 3

So x ∈ (– `oo,` – 7) ∪ (3, `oo`)