Q5 of 122 Page 15

Solve each of the following system of inequations in R

3x – 6 > 0, 2x – 5 > 0

Given 3x – 6 > 0 and 2x – 5 > 0


Let us consider the first inequality.


3x – 6 > 0


⇒ 3x – 6 + 6 > 0 + 6


⇒ 3x > 6



⇒ x > 2


∴ x ∈ ( 2, ∞) (1)


Now, let us consider the second inequality.


2x – 5 > 0


⇒ 2x – 5 + 5 > 0 + 5


⇒ 2x > 5




(2)


From (1) and (2), we get




Thus, the solution of the given system of inequations is


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