If \(|2z| - 1 \ge 2,\) which of the following graphs could be a number line representing all the possible values of z?

[Gmat_mission]

If \(|2z| - 1 \ge 2,\) which of the graphs above could be a number line representing all the possible values of \(z?\)

Answer: A

Source: Manhattan GMAT

[kapil.1]

Step 1: Simplifying the inequality
|2z| -1 ≥ 2
Adding 1 to both the sides
|2z| ≥ 3

hence, 2z ≥ 3 and 2z ≤ -3
= z ≥ 3/2 and z ≤ -3/2
= z ≥ 1.5 and z ≤ -1.5

A is correct