Since, the points (1,2) and (3,4) lie on the same side of the line 3x−5y+a=0 ∴ 3(1)−5(2)+a≥0 or ≤0 ⇒ a−7≥0 or ≤0 ⇒ a≥7 or a≤7 and 3(3)−5(4)+a≥0 or ≤0 ⇒ a−11≥0 or ≤0 ⇒ a≥11 or a≤11 So, common condition is [7,11].