Question

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.

Answer 1

P = {x : 7x – 4 > 5x + 2, x ∈ R}

7x – 4 > 5x + 2

7x – 5x > 2 + 4

2x > 6

x > 3

Q = {x : x – 19 ≥ 1 – 3x, x ∈ R}

x – 19 ≥ 1 – 3x

x + 3x ≥ 1 + 19

4x ≥ 20

x ≥ 5

P ∩ Q = {x : x ≥ 5, x ∈ R}