Question

Solve the following inequalities and graph their solution set
A = {x : 11x -5 ≥ 7x + 3, x ∈ R} and
B = {x : 18x - 9 ≥ 15 + 12x, x ∈ R}

Answer 1

A = {x : 11x -5 ≥ 7x + 3, x ∈ R}
= {x : 11x - 7x ≥ 3 + 5, x ∈ R}
= {x : 4x ≥ 8, x ∈ R}
= {x : x ≥ 2, x ∈ R}        ...(i)
Also B = {x : 18x - 9 ≥ 15 + 12x, x ∈ R}
= {x : 18x - 12x ≥ 15 + 9, x ∈ R}
= (x : 6x ≥ 24, x ∈ R}
= {x : x ≥ 4, x ∈ R}       ...(ii)
∴ on number line,

∴ A ∩ B : {x : x ≥ 4, x ∈ R} 
i.e. A ∩ B :