Answer :

Given –5 < 2x – 3 < 5


The above inequality can be split into two inequalities.


–5 < 2x – 3 and 2x – 3 < 5


Let us consider the first inequality.


–5 < 2x – 3


2x – 3 > –5


2x – 3 + 3 > –5 + 3


2x > –2



x > –1


x (–1, ∞) (1)


Now, let us consider the second inequality.


2x – 3 < 5


2x – 3 + 3 < 5 + 3


2x < 8



x < 4


x > –2


x (–∞, 4) (2)


From (1) and (2), we get


x (–1, ∞) (–∞, 4)


x (–1, 4)


Thus, the solution of the given system of inequations is (–1, 4).


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