# How do you find the x intercepts for y - 2 = - | x + 3 | + 1?

May 6, 2017

$x = - 6 , x = 0$

#### Explanation:

$\text{to find the x-intercepts}$

• " let y = 0, in the equation"

$y - 2 = - | x + 3 | + 1$

$\text{add 2 to both sides}$

$y \cancel{- 2} \cancel{+ 2} = - | x + 3 | + 1 + 2$

$\Rightarrow y = - | x + 3 | + 3$

$y = 0 \to - | x + 3 | + 3 = 0$

$\textcolor{b l u e}{\text{Isolate"" the absolute value}}$

$\Rightarrow - | x + 3 | = - 3$

$\text{multiply both sides by - 1}$

$\Rightarrow | x + 3 | = 3$

$\text{there are 2 possible solutions to the equation}$

$\Rightarrow x + 3 = \textcolor{red}{\pm} 3$

$\textcolor{b l u e}{\text{First solution}}$

$x + 3 = \textcolor{red}{+} 3$

$\text{subtract 3 from both sides}$

$\Rightarrow x = 3 - 3 = 0 \leftarrow \textcolor{m a \ge n t a}{\text{ x-intercept}}$

$\textcolor{b l u e}{\text{Second solution}}$

$x + 3 = \textcolor{red}{-} 3$

$\text{subtract 3 from both sides}$

$\Rightarrow x = - 6 \leftarrow \textcolor{m a \ge n t a}{\text{ x-intercept}}$
graph{-|x+3|+3 [-10, 10, -5, 5]}