# How do you solve the graph: 1<3x-2≤10?

Oct 2, 2015

$1 < x \le 4$
as a line graph:

#### Explanation:

Given an inequality, you can
- add the same amount to both sides
- divide both sides by any amount greater than zero
without effecting the validity or orientation of the inequality

$1 < 3 x - 2 \le 10$

can be split into two inequalities

$1 < 3 x - 2$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow 3 < 3 x$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow 1 < x$

and

$3 x - 2 \le 10$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow 3 x \le 12$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow x \le 4$