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?
You have to be careful when multiplying by x since x might be negative and hence flip the inequality. Suppose x>0. Then
If x>0 and x>1/4, then x>1/4.
Now suppose x<0. Then
If x<0 and x<1/4, then x<0.
So the solution set is (−∞,0)∪(1/4,∞).