# How do you solve 1< 3x - 2\leq 10?

Jun 16, 2018

See a solution process below:

#### Explanation:

First, add $\textcolor{red}{2}$ to each segment of the system of inequalities to isolate the $x$ term while keeping the system balanced:

$1 + \textcolor{red}{2} < 3 x - 2 + \textcolor{red}{2} \le 10 + \textcolor{red}{2}$

$3 < 3 x - 0 \le 12$

$3 < 3 x \le 12$

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

$\frac{3}{\textcolor{red}{3}} < \frac{3 x}{\textcolor{red}{3}} \le \frac{12}{\textcolor{red}{3}}$

$1 < \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} x}{\cancel{\textcolor{red}{3}}} \le 4$

$1 < x \le 4$

Or

$x > 1$; $x \le 4$

Or, in interval notation:

$\left(1 , 4\right]$