Question

Let A = {x ∈ R : 11x – 5 > 7x + 3} and B = {x ∈ R : 8x – 9 ≥ 15 + 2x}.

Find A ∩ B and represent it on the number line.

[Hint: A = {x ∈ R : x > 2} and B = {x ∈ R : x ≥ 4). So, A ∩ B = {x ∈ R : x ≥ 4}.]

Answer 1

Given,

A = {x ∈ R : 11x – 5 > 7x + 3}

⇒ 11x – 5 > 7x + 3

⇒ 11x – 7x > 3 + 5

⇒ 4x > 8

⇒ `x > 8/4`

⇒ x > 2

Since, x ∈ R,

A = {x : x > 2, x ∈ R}

Given,

B = {x ∈ R : 8x – 9 ≥ 15 + 2x}

⇒ 8x – 9 ≥ 15 + 2x

⇒ 8x – 2x ≥ 15 + 9

⇒ 6x ≥ 24

⇒ `x ≥ 24/6`

⇒ x ≥ 4

Since, x ∈ R

B = {x : x ≥ 4, x ∈ R}

A ∩ B = Numbers common between A and B = {x : x ≥ 4, x ∈ R}

Hence, A ∩ B = {x : x ≥ 4, x ∈ R}.

Solution on the number line is: