How do you solve and write the following in interval notation: 8- 5x<=23?

May 25, 2017

$\left[- 3 , + \infty\right)$

Explanation:

$\text{Isolate " -5x" by subtracting 8 from both sides}$

$\cancel{8} \cancel{- 8} - 5 x \le 23 - 8$

$\Rightarrow - 5 x \le 15$

$\text{divide both sides by - 5}$

$\textcolor{b l u e}{\text{Note ""when multiplying/dividing an inequality}}$
$\text{by a negative quantity, the inequality sign is "color(red)"reversed}$

$\frac{\cancel{- 5} x}{\cancel{- 5}} \ge \frac{15}{- 5} \leftarrow \textcolor{red}{\text{ reverse sign}}$

$\Rightarrow x \ge - 3 \text{ is the solution}$

$\left[- 3 , + \infty\right) \leftarrow \text{ in interval notation}$