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:

(i) P ∩ Q

(ii) P – Q

(iii) P ∩ Q’ on different number 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

(i) P ∩ Q = {x : x ≥ 5, x ∈ R}

(ii) P – Q = { X : 1 < X < 5, X ∈ R}

(iii) P ∩ Q’ = {x : 1 < x < 5, x ∈ R}