Hey all,
I am having problems trying to figure out the following inequality. 1/x<2. I keep getting inverse x and not sure how to proceed from there.
You can't do that Pickslides, because you don't know if $\displaystyle \displaystyle x$ is positive or negative. You will need to consider each case.
Case 1: $\displaystyle \displaystyle x < 0$...
Clearly $\displaystyle \displaystyle \frac{1}{x} < 0$, and therefore $\displaystyle \displaystyle < 2$.
So $\displaystyle \displaystyle x < 0$ satisfies the inequality.
Case 2: $\displaystyle \displaystyle x > 0$...
$\displaystyle \displaystyle \frac{1}{x} < 2$
$\displaystyle \displaystyle 1 < 2x$
$\displaystyle \displaystyle \frac{1}{2} < x$.
So the solution is $\displaystyle \displaystyle x \in (-\infty, 0) \cup \left(\frac{1}{2}, \infty\right)$.