Question

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

Answer 1

A = {x : 11x – 5 > 7x + 3, x ∈R}
B = {x : 18x – 9 ≥ 15 + 12x, x ∈R}
Now, A = 11x – 5 > 7x + 3
⇒ 11x – 7x > 3 + 5
⇒ 4x > 8
⇒ x > 2, x ∈ R
B = 18x - 9 ≥ 15 + 12x
⇒  18x - 12x ≥ 15 + 9
⇒ 6x ≥ 24
⇒ x ≥ 4
∴ A ∩ B = x ≥ 4, x ∈ R
Hence Range of A ∩ B = {x : x ≥ 4, x ∈ R} and its graph will be.