Solving 1x<4 gives me x>14. The book however states the answer is: x<0 or x>14.

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?

**Answer**

You have to be careful when multiplying by x since x might be negative and hence flip the inequality. Suppose x>0. Then

1x<4⟺4x>1⟺x>1/4.

If x>0 and x>1/4, then x>1/4.

Now suppose x<0. Then

1x<4⟺4x<1⟺x<1/4.

If x<0 and x<1/4, then x<0.

So the solution set is (−∞,0)∪(1/4,∞).

**Attribution***Source : Link , Question Author : Augusto Dias Noronha , Answer Author : Sri-Amirthan Theivendran*