Question

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.

Answer 1

A = {x: 11x - 5 > 7x + 3, x ∈ R}

= {x : 4x > 8, x ∈ R}

= {x : x > 2, x ∈ R}

B = {x : 18x - 9 ≥ 15 + 12x, x ∈ R}

= {x : 6x ≥ 24, x ∈ R}

= {x : x ≥ 4, x ∈ R}

A ∩ B = {x : x ≥ 4, x ∈ R}

It can be represented on number line as: