# How do solve 5/x>3 and write the answer as a inequality and interval notation?

Mar 2, 2017

$\frac{5}{3} > x$ or $\textcolor{b l u e}{x < \frac{5}{3}}$ and $\left(0 , \frac{5}{3}\right)$

#### Explanation:

$\left(\frac{5}{x} > 3\right)$ as in equalities, can be multiplied on both sides by $x$ then divided on both sides by $3$

$5 > 3 x$

$\frac{5}{3} > x$ is the inequality.

The question gives us a hint in answering the interval notation part, because we can see right away that $x = 0$ is undefined and so it must be excluded color(red)(( as an endpoint.

Since there are no negative numbers given, we are not concerned about endpoints less than $0$.

We can also see from our solution above that $\frac{5}{3} = x$ cannot exist so 5/3 is an excluded color(red)) endpoint.

Then the interval notation is $\left(0 , \frac{5}{3}\right)$.

This means x can be $1$ or any fraction between $0$ and $\frac{5}{3}$, but it cannot be $0$ or $\frac{5}{3}$.

Note that when you reverse components in the equality from one side to $\textcolor{b l u e}{t h e o t h e r s i \mathrm{de}}$ as in the answer above, it is necessary to REVERSE the sign of the inequality at the same time.