Question

Sketch the graph which represents the solution set for the following inequation.
|x| ≥ 3.5

Answer 1

|x| ≥ 3.5
⇒ x ≥ 3.5 or x ≤ −3.5
Here, x takes values greater than or equal to 3.5, or it takes values less than or equal to −3.5
∴ Solution set represents the unbounded (semi-left closed) interval [3.5, ∞] or the unbounded (semi-right closed) interval [− ∞, -3.5]
∴ x ∈ [−∞, −3.5] ∪ [3.5, ∞] 
∴ the required graph of the solution set is as follows: