Question

If A = {x : 11x – 5 > 7x + 3, x ∈ R} and B = {x : 15 + 12x ≤ 18x – 9, x ∈ R}, find the range of set A ∩ B and represent it on the number line.

Answer 1

Given:

Set A = {x : 11x − 5 > 7x + 3, x ∈ R}

Set B = {x : 15 + 12x ≤ 18x − 9, x ∈ R}

Set A

11x − 5 > 7x + 3

⇒ 11x − 7x > 3 + 5

⇒ 4x > 8

⇒ x > 2

A = {x ∈ R : x > 2}

Set B

15 + 12x ≤ 18x − 9

⇒12x − 18x ≤ − 9 − 15

⇒ −6x ≤ − 24

⇒ x ≥ 4

B = {x ∈ R : x ≥ 4}

A = (2, ∞), B = (4, ∞)

A ∩ B = (4, ∞)​