# How do you solve -\frac { x } { 6} + \frac { 22} { 6} \leq - \frac { 6x } { 3}?

Oct 24, 2017

$x \le - 2$

#### Explanation:

$\text{multiply ALL terms on both sides of the inequality by the}$
$\textcolor{b l u e}{\text{lowest common multiple ""of 6 and 3}}$

$\text{the lowest common multiple of 6 and 3 is } 6$

(cancel(6)xx-x/cancel(6))+(cancel(6)xx22/cancel(6)) <=cancel(6)^2xx-(6x)/cancel(3)^1)

$\Rightarrow - x + 22 \le - 12 x \leftarrow \textcolor{b l u e}{\text{ no fractions}}$

$\text{add 12x to both sides}$

$- x + 12 x + 22 \le \cancel{- 12 x} \cancel{+ 12 x}$

$\Rightarrow 11 x + 22 \le 0$

$\text{subtract 22 from both sides}$

$11 x \cancel{+ 22} \cancel{- 22} \le 0 - 22$

$\Rightarrow 11 x \le - 22$

$\text{divide both sides by 11}$

$\frac{\cancel{11} x}{\cancel{11}} \le \frac{- 22}{11}$

$\Rightarrow x \le - 2 \text{ is the solution}$