# How do you solve -24<= -6(-2p-8)?

Nov 30, 2016

$p \ge - 6$

#### Explanation:

First, expand the term withing parenthesis. Remember a negative number times a negative number results in a positive number:

$- 24 \le \left(- 6 \cdot - 2 p\right) + \left(- 6 \cdot - 8\right)$

$- 24 \le 12 p + 48$

Now subtract 48 from each side of the inequality to isolate the $p$ term and keep the inequality balanced:

$- 24 - 48 \le 12 p + 48 - 48$

$- 72 \le 12 p + 0$

$- 72 \le 12 p$

Now we need to divide each side of the equation by $12$ to slve for $p$ and keep the inequality balanced:

$\frac{- 72}{12} \le \frac{12 p}{12}$

$- 6 \le \frac{\cancel{12} p}{\cancel{12}}$

$- 6 \le p$

Finally, to solve in terms of $p$ we can reverse or flip the inequality:

$p \ge - 6$