Question

If P = {x : 7x - 4 > 5x + 2, x ∈  R} and Q - {x : x - 19 ≥ 1 - 3x, x ∈ R}, represent the following solution set on different number lines: 

P' ∩ Q

Answer 1

P = {x : 7x - 4 > 5x + 2, x ∈  R}

7x- 4 > 5x+2

7x-5x > 2+ 4

2x > 6

X > 3

p = { 4, 5, 6, 7,.........}

and 

Q - {x : x - 19 ≥ 1 - 3x, x ∈ R}

x - 19 ≥ 1 - 3x

x + 3x ≥ 1+19

4x ≥ 20

x ≥ s

Q = {5,6, 7, 8, 9 ........ } 

P' ∩ Q = { `phi` }