# How do you solve the compound inequalities 9 + 3n>=6 or 5n < 25?

May 4, 2015

Handle each inequality separately and then recombine.

$9 + 3 n \ge 6$
$\rightarrow n \ge - 1$

$5 n < 25$
$\rightarrow n < 5$

So $9 + 3 n \ge 6 \text{ or } 5 n < 25$
is equivalent to
$n \ge - 1 \text{ or } n < 5$

But one or the other is true for any Real value of $n$
So
$n \epsilon \left(- \infty , + \infty\right)$