# How do you solve and write the following in interval notation: 5-y>=4?

Jun 23, 2017

$\left(- \infty , 1\right]$

#### Explanation:

$\text{subtract 5 from both sides}$

$\cancel{5} \cancel{- 5} - y \ge 4 - 5$

$\Rightarrow - y \ge - 1$

$\text{multiply through by - 1}$

$\textcolor{b l u e}{\text{NOTE}}$ when multiplying/dividing by a negative quantity $\textcolor{red}{\text{Reverse}}$ the inequality symbol.

$\Rightarrow y \le 1 \leftarrow \textcolor{red}{\text{ reverse symbol}}$

$\text{in interval notation } \left(- \infty , 1\right]$

Jun 23, 2017

Solution: $y \le 1$. In interval notation : $\left(- \infty , 1\right]$
$5 - y \ge 4 \mathmr{and} - y \ge 4 - 5 \mathmr{and} - y \ge - 1 \mathmr{and} y \le 1$
Solution: $y \le 1$. In interval notation : $\left(- \infty , 1\right]$ [Ans]