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)