We have to find values of x for which both the equations hold true

x – 2 ≥ 0 and 2x – 5 ≤ 3

we will solve both the equations separately and then their intersection set will be solution of the system

x – 2 ≥ 0

⇒ x ≥ 2

Hence x ∈ (2, ∞)

Now, 2x – 5 ≤ 3

⇒ 2x ≤ 3 + 5

⇒ 2x ≤ 8

⇒ x ≤ 4

Hence x ∈ (-∞, 4)

The intersection of set (2, ∞) and (-∞, 4) is (2, 4)

Representing on number line

Hence solution set for given system of equation is x ∈ (2, 4)