# How do you solve and write the following in interval notation: -16x - 8 ≤ -4(3x +1)?

Jun 15, 2017

$\left[- 1 , + \infty\right)$

#### Explanation:

$\text{distribute the bracket on the right side}$

$- 16 x - 8 \le - 12 x - 4$

$\text{add 16x to both sides}$

$\cancel{- 16 x} \cancel{+ 16 x} - 8 \le - 12 x + 16 x - 4$

$\Rightarrow - 8 \le 4 x - 4$

$\text{add 4 to both sides}$

$- 8 + 4 \le 4 x \cancel{- 4} \cancel{+ 4}$

$\Rightarrow - 4 \le 4 x$

$\text{divide both sides by 4}$

$- \frac{4}{4} \le \frac{\cancel{4} x}{\cancel{4}}$

$\Rightarrow - 1 \le x \Rightarrow x \ge - 1$

$\text{in interval notation } \left[- 1 , + \infty\right)$