Writing solutions of inequalities: $3<x$ versus $x>3$

Question

My son wrote a solution to a number line graph as 3 < x instead of what his teacher said was the correct answer of x > 3. When he brought his paper back in to bring it up he was told that the variable had to come first. I can't imagine why this is so - is there any precedence for this one-sided interpretation? As a former math teacher I am perplexed why someone would not allow for an alternate writing (albeit an odd one).

Answer 1

$3<x \iff x>3$.

That is, the statements $3<x$ and $x>3$ are equivalent.

Your son's teacher is wrong.

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I personally prefer to put the variable first, but, by no means is not doing so wrong. It's just a matter of convention.

The reason for the teacher's wanting to put the variable first is that it's more natural to express the solution, $x$, in terms of 3 in this case. We don't really care about what 3 is in terms of anything else; we care about what $x$ is, which is why we usually put $x$ first.

Answer 2

The object of the sentence $3<x$ is 3 but really the object we are interested in is $x$ so $x>3$ is preferable. Also, graphing $3<x$ is conceptually more difficult at that level and so the preference is $x>3$. A frequent error is to graph the wrong solution, showing that the student doesn't understand the answer. His answer is correct, just not preferred. As in 1/2 is preferred over 2/4.