How do you solve abs(y+3)+4=20?

Jun 10, 2017

$y = - 19 \text{ or } y = 13$

Explanation:

$\text{Isolate " |y+3|" by subtracting 4 from both sides}$

$| y + 3 | \cancel{+ 4} \cancel{- 4} = 20 - 4$

$\Rightarrow | y + 3 | = 16$

$\text{the expression inside the absolute value can be positive or}$
$\text{negative}$

$\Rightarrow y + 3 = 16 \to y = 16 - 3 = 13 \leftarrow \left(\textcolor{red}{1}\right) \text{ or }$

$- \left(y + 3\right) = 16$

$\Rightarrow - y - 3 = 16 \to - y = 16 + 3 \to y = - 19 \leftarrow \left(\textcolor{red}{2}\right)$

$\textcolor{b l u e}{\text{As a check}}$

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

$y = 13 \to | 13 + 3 | + 4 = | 16 | + 4 = 16 + 4 = 20$

$y = - 19 \to | - 19 + 3 | + 4 = | - 16 | + 4 = 20$

$\Rightarrow y = - 19 \text{ or " y=13" are the solutions}$