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you take a positive value of that particular number then it will gives a positive value only.

3 x + 5 < 9 or, 3 x < 4 or, x < 4 / 3 … (1)

Again, if 3 x + 5 < 0, then | 3 x + 5 | < 9 gives

- (3 x + 5) < 9 or, - 3x < 14 or, x > - 14 / 3 … (2)

Therefore from (1) and (2) we get, -14 / 3 < x < 4 / 3, which is required solution of the given inequalities.

-3< (x + 1) < 3

-3 – 1 < x < 3 – 1

- 4 < x < 2

-1 < (2 x – 7) < 1

-1 + 7 < 2 x < 1 + 7

6 < 2 x < 8

3 < x < 4