Samantha N.

# Solve. Write the solution set in interval notation. (Enter EMPTY or Ø for the empty set.) 3x + 7 < 10 or 6x - 14 > 4

use set in interval notation

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Imtiazur S.

Thanks for pointing that out Kim.  I missed that.  When you have a system of inequalities it is generally an AND and in this case there is clearly an OR which changes the set contents.
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09/09/13

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Imtiazur S.

I like the solution but I have a minor correction I must point out.  In set notation it is always a parenthesis on -∞ and ∞ and a square bracket should not be used because those are not real numbers and cannot actually be inclusive in the set.  So your solution should be rewritten as (-∞;1)∪(3;∞).  Even 1 and 3 are not inclusive so use parentheses all the way.
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09/09/13

Isabelle G.

Thanks for the explanation.
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09/09/13

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Bam K.

It's interesting to read the issues raised by the conjunction or in the treatment of this appearently simple problem. Semantics do matter in Math! Kirill took in account the two interpretations that can legitimately be attributed to the author of the question through its use of the conditional If .

Very often, students who post their questions are unaware of the implications of ambiguous statements leading to interpretations of what they really want. I considered the option of satisfying the two inequalities simultaneously, showing through work how to solve separately each inequality.

The final arbitrator would be the author's intention and question unambiguously stated.
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09/10/13

Imtiazur S.

Bam brings a good point.  I agree with the fact that the students are unaware of the implications of the little things in a problem, but they need to see the correct solution based on the question they posted, which, in some cases is copied and pasted from the original text.  In my opinion, the solution must present all arguments within the solution being provided and sometimes even the meaning of the question should be stated in the solution so that the student understands the problem and the solution.  In this question, the plain English interpretation of the problem is "find all possible values of x for which either 3x+7 is less than 10 or 6x-14 is greater than 4".  I believe tutors who provide answers do not always do a good job of this.
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09/10/13

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