As a simple example, say I'm trying to derive the upper bound of a confidence interval for the mean. That is, I'm trying to solve for $\mu$ in
$$ \frac{\bar{X} - \mu}{\frac{\sigma}{\sqrt{n}}} < Z_{\frac{\alpha}{2}} $$
If I tell Wolfram Alpha solve (x - mu) / (sigma/sqrt(n)) = z for mu, then it gives an answer which is correct.
However, if I tell Wolfram Alpha solve (x - mu) / (sigma/sqrt(n)) < z for mu, then I don't.
Can anyone explain what's going on?
A priori, the consequent bound on $\mu$ depends on whether $\sigma > 0$ or $\sigma < 0$. As an artefact of whatever procedure Wolfram Alpha uses, (currently) it also breaks up the cases where $z \ge 0$ and where $z < 0$, even though the answer does not actually depend on this.
From the question title, I'm guessing you know that $\sigma > 0$. If you add this assumption to the query you get the correct answer, though still split up into cases depending on the sign of $z$.