Given and 2(2x + 3) < 6(x – 2) + 10

Let us consider the first inequality.

⇒ 3(2x – 11) ≥ 4(4x – 18)

⇒ 6x – 33 ≥ 16x – 72

⇒ 6x – 33 + 33 ≥ 16x – 72 + 33

⇒ 6x ≥ 16x – 39

⇒ 16x – 39 ≤ 6x

⇒ 16x – 39 + 39 ≤ 6x + 39

⇒ 16x ≤ 6x + 39

⇒ 16x – 6x ≤ 6x + 39 – 6x

⇒ 10x ≤ 39

(1)

Now, let us consider the second inequality.

2(2x + 3) < 6(x – 2) + 10

⇒ 4x + 6 < 6x – 12 + 10

⇒ 4x + 6 < 6x – 2

⇒ 4x + 6 – 6 < 6x – 2 – 6

⇒ 4x < 6x – 8

⇒ 6x – 8 > 4x

⇒ 6x – 8 + 8 > 4x + 8

⇒ 6x > 4x + 8

⇒ 6x – 4x > 4x + 8 – 4x

⇒ 2x > 8

⇒ x > 4

∴ x ∈ (4, ∞) (2)

From (1) and (2), we get

∴ x ∈ ∅

Thus, there is no solution of the given system of inequations.