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Pitrellais 2022-05-21 Answered
Elementary system of inequalities - set of solutions
3 x 1 1 + 4 x
5 6 x + 2 3 1 + 1 2 x
x 1 6 < 1 4

x 2
x 1
x < 5 2
I compared the above reduced inequalities which gave me as answer that the solutions are from [ 5 2 ]. I think it is correct but I'm not sure. Can someone affirm this or debunk this please and what's the reason?
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Answers (1)

Louis Lawrence
Answered 2022-05-22 Author has 10 answers
The x 1 trumps the x 2 so your solution set is [ 1 , 5 2 ).
To find the solution set, you take the intersection of each solution set.
x 2 has solution set [ 2 , )
x 1 has solution set [ 1 , )
x < 5 2 has solution set ( , 5 2 )
The intersection of [ 2 , ) and [ 1 , ) is [ 1 , ) because 2 < 1. Furthermore, the intersection of [ 1 , ) and ( , 5 2 ) is [ 1 , 5 2 ).
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