# How do you solve -3(7n+3)<6n?

Jan 24, 2017

See the entire solution process below:

#### Explanation:

First, expand the term in parenthesis:

$- 3 \left(7 n + 3\right) < 6 n$

$- 21 n - 9 < 6 n$

Now, add $\textcolor{red}{21 n}$ to each side of the inequality to isolate the $n$ term while keeping the inequality balanced:

$- 21 n - 9 + \textcolor{red}{21 n} < 6 n + \textcolor{red}{21 n}$

$- 21 n + \textcolor{red}{21 n} - 9 < \left(6 + 21\right) n$

$0 - 9 < 27 n$

$- 9 < 27 n$

Next, divide each side of the inequality by $\textcolor{red}{27}$ to solve for $n$ while keeping the inequality balanced:

$- \frac{9}{\textcolor{red}{27}} < \frac{27 n}{\textcolor{red}{27}}$

$- \frac{1}{3} < \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{27}}} n}{\cancel{\textcolor{red}{27}}}$

$- \frac{1}{3} < n$

And to solve in terms of $n$ we reverse or "flip" the inequality:

$n > - \frac{1}{3}$