Question

P is the solution set of 7x – 2 > 4x + 1 and Q is the solution set of 9x – 45 ≥ 5(x – 5); where x ∈ R. Represent:

1. P ∩ Q
2. P – Q
3. P ∩ Q’ on the different number of lines.

Answer 1

P = {x : 7x – 2 > 4x + 1, x ∈ R}

7x – 2 > 4x + 1

7x – 4x > 1 + 2

3x > 3

x > 1

and

Q = {x : 9x – 45 ≥ 5(x – 5), x ∈ R}

9x – 45 ≥ 5x – 25

9x – 5x ≥ –25 + 45

4x ≥ 20

x ≥ 5

1.  P ∩ Q = {x : x ≥ 5, x ∈ R}

2. P – Q = {x : 1 < x < 5, x ∈ R}

3. P ∩ Q' = {x : 1 > x < 5, x ∈ R}