Solve each of the following system of inequations in R

x – 2 > 0, 3x < 18

Given x – 2 > 0 and 3x < 18


Let us consider the first inequality.


x – 2 < 0


x – 2 + 2 < 0 + 2


x < 2


x ( 2, ∞) (1)


Now, let us consider the second inequality.


3x < 18



x < 6


x (–∞, 6) (2)


From (1) and (2), we get


x (2, ∞) (–∞, 6)


x ( 2, 6)


Thus, the solution of the given system of inequations is (2, 6).


3