Inspired by Svatejas Shivakumar

Algebra Level 3

True or false :

$\quad$ The solution set to $\dfrac{1}{x} < 1$ is $1 < x$ .

True False

3 solutions

Hana Wehbi
May 22, 2016

We just need a counter example to prove it is false. Take $x=-2$ for instance, then $\frac{-1}{2}$ $<1$ , but $-2<1$

Sabhrant Sachan
May 22, 2016

$\dfrac1{x}<1 \\ \dfrac1{x}-1<0 \\ \dfrac{(1-x)}{x}<0 \\ \dfrac{(x-1)}{(x-0)}>0 \\ \text{Using wavy curve method } x \in (-\infty,0) \cup (1,\infty)$

Use LaTeX \cup in place of U else nice solution :)

Ashish Menon - 5 years ago

thanks for the help :)

Sabhrant Sachan - 5 years ago

J D
May 22, 2016

It is X<1 or X<0