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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.
Solution
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}
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