Question

If P = {x : 7x - 2 > 4x + 1, x ∈  R} and Q = {x : 9x - 45 ≥  5 (x -5),x ∈ R} , represent the following solution set on different number lines: 

P ∩ Q'

Answer 1

P = {x : 7x - 2 > 4x + 1, x ∈  R}

7x - 2 > 4x + 1

7X - 4X >1 + 2 

3x > 3

X>1

p = {2,3, 4, 5. ···········}

and  

Q = {x : 9x - 45 ≥  5 (x -5) ,x ∈ R}

9x - 45  ≥ 5x - 25 

9x - 5x ≥ -25 + 45 

4x ≥ 20 

x ≥ 5

Q = {5, 6, 7, 8, 9, ............ } 

P ∩ Q' = {6, 7, 8, 9, ........... }