Mathematics
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.
Linear Inequations
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Answer
Given,
P is the solution set of 7x - 2 > 4x + 1
Solving,
⇒ 7x - 2 > 4x + 1
⇒ 7x - 4x > 1 + 2
⇒ 3x > 3
Dividing both sides by 3 we get,
⇒ x > 1
Given,
Q is the solution set of 9x - 45 ≥ 5(x - 5)
Solving,
⇒ 9x - 45 ≥ 5(x - 5)
⇒ 9x - 45 ≥ 5x - 25
⇒ 9x - 5x ≥ -25 + 45
⇒ 4x ≥ 20
Dividing both sides by 4 we get,
⇒ x ≥ 5.
∴ P = {x : x > 1, x ∈ R} and Q = {x : x ≥ 5, x ∈ R}
(i) P ∩ Q = Numbers common between P and Q
∴ Solution set = {x : x ≥ 5, x ∈ R}
Solution on the number line is :
(ii) P - Q = Numbers which belong to P but do not belong to Q
∴ Solution set = {x : 1 < x < 5, x ∈ R}
Solution on the number line is :
(iii) P ∩ Q' = Numbers which belong to P but do not belong to Q
∴ Solution set = {x : 1 < x < 5, x ∈ R}
Solution on the number line is :
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