Answer :

Given 5x – 7 < 3(x + 3) and


Let us consider the first inequality.


5x – 7 < 3(x + 3)


5x – 7 < 3x + 9


5x – 7 + 7 < 3x + 9 + 7


5x < 3x + 16


5x – 3x < 3x + 16 – 3x


2x < 16



x < 8


x (–∞, 8) (1)


Now, let us consider the second inequality.





2 – 3x ≥ 2(x – 4)


2 – 3x ≥ 2x – 8


2 – 3x – 2 ≥ 2x – 8 – 2


–3x ≥ 2x – 10


2x – 10 ≤ –3x


2x – 10 + 10 ≤ –3x + 10


2x ≤ –3x + 10


2x + 3x ≤ –6x + 10 + 6x


5x ≤ 10



x ≤ 2


x (–∞, 2] (2)


From (1) and (2), we get


x (–∞, 8) (–∞, 2]


x (–∞, 2]


Thus, the solution of the given system of inequations is (–∞, 2].


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