Answer :

Given 2(x – 6) < 3x – 7 and 11 – 2x < 6 – x


Let us consider the first inequality.


2(x – 6) < 3x – 7


2x – 12 < 3x – 7


2x – 12 + 12 < 3x – 7 + 12


2x < 3x + 5


3x + 5 > 2x


3x + 5 – 5 > 2x – 5


3x > 2x – 5


3x – 2x > 2x – 5 – 2x


x > –5


x (–5, ∞) (1)


Now, let us consider the second inequality.


11 – 2x < 6 – x


11 – 2x – 11 < 6 – x – 11


–2x < –x – 5


–x – 5 > –2x


–x – 5 + 5 > –2x + 5


–x > –2x + 5


–x + 2x > –2x + 5 + 2x


x > 5


x (5, ∞) (2)


From (1) and (2), we get


x (–5, ∞) (5, ∞)


x (5, ∞)


Thus, the solution of the given system of inequations is (5, ∞).


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