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Question
Given:
A = {x : 11x – 5 > 7x + 3, x ∈ R} and
B = {x : 18x – 9 ≥ 15 + 12x, x ∈ R}.
Find the range of set A ∩ B and represent it on the number line.
Solution
A = {x : 11x – 5 > 7x + 3, x ∈ R}
= {x : 4x > 8, x ∈ R}
= {x : x > 2, x ∈ R}
B = {x : 18x – 9 ≥ 15 + 12x, x ∈ R}
= {x : 6x ≥ 24, x ∈ R}
= {x : x ≥ 4, x ∈ R}
A ∩ B = {x : x ≥ 4, x ∈ R}
It can be represented on number line as:
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