Why does $\frac{1}{x} < 4$ have two answers? Solving $\frac{1}{x} < 4$ gives me $x > \frac{1}{4}$. The book however states the answer is: $x < 0$ or $x > \frac{1}{4}$.
My questions are:
Why does this inequality has two answers (preferably the intuition behind it)?
When using Wolfram Alpha it gives me two answers, but when using $1 < 4x$ it only gives me one answer. Aren't the two forms equivalent?

Here is an important aspect which should be always considered. If someone asks me:

Problem: Find the solution of
  \begin{align*}
\frac{1}{x}<4
\end{align*}
  I would not answer the problem, but instead  ask: What is the domain of $x$?

Please note the problem is not fully specified if the domain of  $x$, the range of validity, is not given. This is crucial to determine the set of solutions.

Some examples:
Find the solution of
\begin{array}{lcl}
\text{domain of }x\qquad&\qquad\text{inequality}\qquad&\qquad\text{solution}\\
\hline\\
\{x|x\in\mathbb{R}\setminus\{0\}\}\qquad&\qquad\frac{1}{x}<4\qquad&\qquad (-\infty,0)\cap(1/4,\infty)\\
\{x|x\in\mathbb{R}^{+}\}\qquad&\qquad\frac{1}{x}<4\qquad&\qquad (1/4,\infty)\\
\{\pi\}\qquad&\qquad\frac{1}{x}<4\qquad&\qquad \{\pi\}\\
\{x|x\in(0,1/4)\}\qquad&\qquad\frac{1}{x}<4\qquad&\qquad \emptyset
\end{array}

Note: If a domain is not explicitly stated in the problem section of a book we should expect a corresponding statement somewhere else at   the beginning of the chapter. 
