# How do you solve and write the following in interval notation: 2x - 3<5 or  3x - 2 >13?

Aug 5, 2017

See a solution process below:

#### Explanation:

Inequality 1:
Start to solve this inequality by adding $\textcolor{red}{3}$ to each side of the inequality to isolate the $x$ term while keeping the inequality balanced:

$2 x - 3 + \textcolor{red}{3} < 5 + \textcolor{red}{3}$

$2 x - 0 < 8$

$2 x < 8$

Now, divide each side of the inequality by $\textcolor{red}{2}$ to solve for $x$ while keeping the inequality balanced:

$\frac{2 x}{\textcolor{red}{2}} < \frac{8}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\cancel{\textcolor{red}{2}}} < 4$

$x < 4$

Inequality 2
Start to solve this inequality by adding $\textcolor{red}{2}$ to each side of the inequality to isolate the $x$ term while keeping the inequality balanced:

$3 x - 2 + \textcolor{red}{2} > 13 + \textcolor{red}{2}$

$3 x - 0 > 15$

$3 x > 15$

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

$\frac{3 x}{\textcolor{red}{3}} > \frac{15}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} x}{\cancel{\textcolor{red}{3}}} > 5$

$x > 5$

**The solution is: $x < 4$ and $x > 5$

Or, in interval notation:

$\left(- \infty , 4\right)$ and $\left(5 , + \infty\right)$