How do you solve 5( - 4n - 4) \leq - 4( 7n + 3) + 6 n?

May 4, 2018

$n \le 4$

Explanation:

$\text{distribute parenthesis on both sides of the inequality}$

$\Rightarrow - 20 n - 20 \le - 28 n - 12 + 6 n$

$\Rightarrow - 20 n - 20 \le - 22 n - 12$

$\text{collect terms in n on the left side and numeric values}$
$\text{on the right side}$

$\text{add "22n" to both sides}$

$- 20 n + 22 n - 20 \le \cancel{- 22 n} \cancel{+ 22 n} - 12$

$\Rightarrow 2 n - 20 \le - 12$

$\text{add 20 to both sides}$

$2 n \cancel{- 20} \cancel{+ 20} \le - 12 + 20$

$\Rightarrow 2 n \le 8$

$\text{divide both sides by 2}$

$\frac{\cancel{2} n}{\cancel{2}} \le \frac{8}{2}$

$\Rightarrow n \le 4 \text{ is the solution}$

$n \in \left(- \infty , 4\right] \leftarrow \textcolor{b l u e}{\text{in interval notation}}$