How do you solve 0<-3N +6 - 12N?

Apr 23, 2017

See the entire solution process below:

Explanation:

First, group and then combine like terms on the right side of the inequality:

$0 < - 3 N + 6 - 12 N$

$0 < - 3 N - 12 N + 6$

$0 < \left(- 3 - 12\right) N + 6$

$0 < - 15 N + 6$

Next, subtract $\textcolor{red}{6}$ from each side of the inequality to isolate the $N$ term while keeping the inequality balanced:

$0 - \textcolor{red}{6} < - 15 N + 6 - \textcolor{red}{6}$

$- 6 < - 15 N + 0$

$- 6 < - 15 N$

Now, divide each side of the inequality by $\textcolor{b l u e}{- 15}$ to solve for $N$ while keeping the inequality balanced. However, because we are multiplying or dividing and inequality by a negative term we must reverse the inequality operator:

$\frac{- 6}{\textcolor{b l u e}{- 15}} \textcolor{red}{>} \frac{- 15 N}{\textcolor{b l u e}{- 15}}$

$\frac{- 3 \times 2}{\textcolor{b l u e}{- 3 \times 5}} \textcolor{red}{>} \frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{- 15}}} N}{\cancel{\textcolor{b l u e}{- 15}}}$

$\frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{- 3}}} \times 2}{\textcolor{b l u e}{\textcolor{b l a c k}{\cancel{\textcolor{b l u e}{- 3}}} \times 5}} \textcolor{red}{>} N$

$\frac{2}{5} > N$

To state the solution in terms of $N$ we can reverse or "flip" the entire inequality:

$N < \frac{2}{5}$