Given :

A = {x : 11x - 5 > 7x + 3, x ∈ R} and

B = {x : 18x - 9 ≥ 15 + 12x, x ∈ R}.

Find the range of set A ∩ B and represent it on a number line.

Given, A = {x : 11x - 5 > 7x + 3, x ∈ R}

Solving, 11x - 5 > 7x + 3

⇒ 11x - 7x > 3 + 5

⇒ 4x > 8

⇒ x > 2

∴ A = {x : x > 2, x ∈ R}

Solving, 18x - 9 ≥ 15 + 12x

⇒ 18x - 12x ≥ 15 + 9

⇒ 6x ≥ 24

Dividing both sides by 6 we get,

⇒ x ≥ 4

∴ B = {x : x ≥ 4, x ∈ R}

A ∩ B = Elements common to both A and B.

Hence, A ∩ B = {x : x ≥ 4, x ∈ R}.

A ∩ B on the number line is :