If P = {x : 7x - 4 > 5x + 2, x ∈ R} and Q = {x : x - 19 ≥ 1 - 3x, x ∈ R}; find the range of set P ∩ Q and represent it on a number line.

Solving 7x - 4 > 5x + 2,

⇒ 7x - 5x > 2 + 4

⇒ 2x > 6

⇒ x > 3.

P = {x : x > 3, x ∈ R}

Solving x - 19 ≥ 1 - 3x

⇒ x + 3x ≥ 1 + 19

⇒ 4x ≥ 20

⇒ x ≥ 5.

Q = {x : x ≥ 5, x ∈ R}

P ∩ Q = Numbers common between P and Q

= {x : x ≥ 5, x ∈ R}

P ∩ Q on the number line is :