# How do you solve and write the following in interval notation: 7x + 8 <14x - 9?

Mar 14, 2018

See a solution process below:

#### Explanation:

First, subtract $\textcolor{red}{7 x}$ and add $\textcolor{b l u e}{9}$ to each side of the inequality to isolate the $x$ term while keeping the inequality balanced:

$7 x - \textcolor{red}{7 x} + 8 + \textcolor{b l u e}{9} < 14 x - \textcolor{red}{7 x} - 9 + \textcolor{b l u e}{9}$

$0 + 17 < \left(14 - \textcolor{red}{7}\right) x - 0$

$17 < 7 x$

Now, divide each side of the equation by $\textcolor{red}{7}$ to solve for $x$ while keeping the equation balanced:

$\frac{17}{\textcolor{red}{7}} < \frac{7 x}{\textcolor{red}{7}}$

$\frac{17}{7} < \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} x}{\cancel{\textcolor{red}{7}}}$

$\frac{17}{7} < x$

We can reverse or "flip" the entire inequality to state the result in terms of $x$:

$x > \frac{17}{7}$

Because $x$ can be any value from $\frac{17}{7}$ but not including $\frac{17}{7}$ to infinity we can write this in interval notation as:

$x = \left(\frac{17}{7} , + \infty\right)$