# How do you solve and write the following in interval notation: -2/5< -4/5x?

May 19, 2017

See a solution process below:

#### Explanation:

Multiply each side of the inequality by color(blue)((5/-4) to solve for $x$ while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:

$\textcolor{b l u e}{\frac{5}{-} 4} \times \frac{- 2}{5} \textcolor{red}{>} \textcolor{b l u e}{\frac{5}{-} 4} \times \frac{- 4}{5} x$

$\frac{- 10}{-} 20 \textcolor{red}{>} \textcolor{b l u e}{\frac{\textcolor{b l a c k}{\cancel{\textcolor{b l u e}{5}}}}{\textcolor{b l a c k}{\cancel{\textcolor{b l u e}{- 4}}}}} \times \frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{- 4}}}}{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{5}}}} x$

$\frac{1}{2} > x$

Or, to state the inequality in terms of $x$ we can reverse or "flip" the entire inequality:

$x < \frac{1}{2}$

And, in interval notation:

$\left(- \infty , \frac{1}{2}\right)$