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 &lt; 1 4 ⇒ x ≥ − 2 x ≥ 1 x &lt; 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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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    &amp;lt;      1    4    ⇒  x  ≥  −  2  x  ≥  1  x  &amp;lt;      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&#039;m not sure. Can someone affirm this or debunk this please and what&#039;s the reason?

Louis Lawrence · Accepted Answer

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  &amp;lt;      5    2   has solution set   (  −  ∞  ,      5    2    )The intersection of   [  −  2  ,  ∞  ) and   [  1  ,  ∞  ) is   [  1  ,  ∞  ) because   −  2  &amp;lt;  1. Furthermore, the intersection of   [  1  ,  ∞  ) and    (  −  ∞  ,      5    2    ) is   [  1  ,      5    2    ).

Elementary system of inequalities - set of solutions 3 x − 1 ≤<!

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