Mathematics
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.
Linear Inequations
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Answer
Solving 7x - 4 > 5x + 2,
⇒ 7x - 5x > 2 + 4
⇒ 2x > 6
⇒ x > 3.
P = {x : x > 3, x ∈ R}
Solving x - 19 ≥ 1 - 3x
⇒ x + 3x ≥ 1 + 19
⇒ 4x ≥ 20
⇒ x ≥ 5.
Q = {x : x ≥ 5, x ∈ R}
P ∩ Q = Numbers common between P and Q
= {x : x ≥ 5, x ∈ R}
P ∩ Q on the number line is :
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