# How do you solve and write the following in interval notation:  3x – 2 <7 and –3x <= 15?

Aug 24, 2017

Se a solution process below:

#### Explanation:

Solve First Equation For x:

$3 x - 2 < 7$

$3 x - 2 + \textcolor{red}{2} < 7 + \textcolor{red}{2}$

$3 x - 0 < 9$

$3 x < 9$

$\frac{3 x}{\textcolor{red}{3}} < \frac{9}{\textcolor{red}{3}}$

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

$x < 3$

Solve second Equation For x:

$- 3 x \le 15$

$\frac{- 3 x}{\textcolor{b l u e}{- 3}} \textcolor{red}{\ge} \frac{15}{\textcolor{b l u e}{- 3}}$

$\frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{- 3}}} x}{\cancel{\textcolor{b l u e}{- 3}}} \textcolor{red}{\ge} - 5$

$x \textcolor{red}{\ge} - 5$

The Solution Is:

$x \ge - 5$ and $x < 3$

Or, in interval notation:

$\left[- 5 , 3\right)$