# How do you solve and write the following in interval notation: -6x + 2< -3x -12?

Apr 27, 2017

See the entire solution process below:

#### Explanation:

First, add $\textcolor{red}{6 x}$ and $\textcolor{b l u e}{12}$ to each side of the inequality to isolate the $x$ term while keeping the equation balanced:

$\textcolor{red}{6 x} - 6 x + 2 + \textcolor{b l u e}{12} < \textcolor{red}{6 x} - 3 x - 12 + \textcolor{b l u e}{12}$

$0 + 14 < \left(\textcolor{red}{6} - 3\right) x - 0$

$14 < 3 x$

Now, divide each side of the equation by $\textcolor{red}{3}$ to solve for $x$ while keeping the equation balanced:

$\frac{14}{\textcolor{red}{3}} < \frac{3 x}{\textcolor{red}{3}}$

$\frac{14}{3} < \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} x}{\cancel{\textcolor{red}{3}}}$

$\frac{14}{3} < x$

Or, in interval notation:

$\left(- \infty , \frac{14}{3}\right)$