Mathematics
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 a number line.
Linear Inequations
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Answer
Given, A = {x : 11x - 5 > 7x + 3, x ∈ R}
Solving, 11x - 5 > 7x + 3
⇒ 11x - 7x > 3 + 5
⇒ 4x > 8
⇒ x > 2
∴ A = {x : x > 2, x ∈ R}
Solving, 18x - 9 ≥ 15 + 12x
⇒ 18x - 12x ≥ 15 + 9
⇒ 6x ≥ 24
Dividing both sides by 6 we get,
⇒ x ≥ 4
∴ B = {x : x ≥ 4, x ∈ R}
A ∩ B = Elements common to both A and B.
Hence, A ∩ B = {x : x ≥ 4, x ∈ R}.
A ∩ B on the number line is :
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