Given

The above inequality can be split into two inequalities.

and

Let us consider the first inequality.

⇒ 0 < –x

⇒ –x > 0

⇒ x < 0

∴ x ∈ (–∞, 0) (1)

Now, let us consider the second inequality.

⇒ –x < 6

⇒ x > –6

∴ x ∈ (–6, ∞) (2)

From (1) and (2), we get

x ∈ (–∞, 0) ∩ (–6, ∞)

∴ x ∈ (–6, 0)

Thus, the solution of the given system of inequations is (–6, 0).