Answer :

Given and 2(2x + 3) < 6(x – 2) + 10


Let us consider the first inequality.






3(2x – 11) ≥ 4(4x – 18)


6x – 33 ≥ 16x – 72


6x – 33 + 33 ≥ 16x – 72 + 33


6x ≥ 16x – 39


16x – 39 ≤ 6x


16x – 39 + 39 ≤ 6x + 39


16x ≤ 6x + 39


16x – 6x ≤ 6x + 39 – 6x


10x ≤ 39




(1)


Now, let us consider the second inequality.


2(2x + 3) < 6(x – 2) + 10


4x + 6 < 6x – 12 + 10


4x + 6 < 6x – 2


4x + 6 – 6 < 6x – 2 – 6


4x < 6x – 8


6x – 8 > 4x


6x – 8 + 8 > 4x + 8


6x > 4x + 8


6x – 4x > 4x + 8 – 4x


2x > 8



x > 4


x (4, ∞) (2)


From (1) and (2), we get



x


Thus, there is no solution of the given system of inequations.


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