# How do you solve 3| 6m - 4| \leq 12?

Oct 18, 2017

$m \le \frac{4}{3} \mathmr{and} m \ge 0$

#### Explanation:

$3 | 6 m - 4 | \le 12$
Let start by dividing both sides by $\textcolor{red}{3}$
$\frac{\cancel{3} \left(| 6 m - 4 |\right)}{\cancel{\textcolor{red}{3}}} \le \frac{12}{\textcolor{red}{3}}$
$| 6 m - 4 | \le 4$
We know...
$6 m - 4 \le 4 \mathmr{and} 6 m - 4 \ge - 4$
$6 m - 4 \le 4$
Add $\textcolor{red}{4}$ to both sides
$6 m \cancel{- 4} \cancel{\textcolor{red}{+ 4}} \le 4 \textcolor{red}{+ 4}$
$6 m \le 8$
Divide both sides by $\textcolor{red}{6}$ to find $m$
$\frac{\cancel{6} m}{\cancel{\textcolor{red}{6}}} \le \frac{8}{\textcolor{red}{6}}$
$m \le \frac{4}{3}$

Now let solve the second condition
$6 m - 4 \ge - 4$
Add $\textcolor{red}{4}$ to both sides
$6 m \cancel{- 4} \cancel{\textcolor{red}{+ 4}} \ge \cancel{- 4} \cancel{\textcolor{red}{+ 4}}$
$6 m \ge 0$
Divide both sides by $\textcolor{red}{6}$
$\frac{\cancel{6} m}{\cancel{\textcolor{red}{6}}} \ge \frac{0}{\textcolor{red}{6}}$
$m \ge 0$

Thus,
the final answers are $m \le \frac{4}{3} \mathmr{and} m \ge 0$