# Evaluate: |y+3| < 8

## Expression: $|y+3| < 8$

Separate the inequality into $2$ possible cases

$\begin{array} { l }\begin{array} { l }y+3 < 8,& y+3 \geq 0\end{array},\\\begin{array} { l }-\left( y+3 \right) < 8,& y+3 < 0\end{array}\end{array}$

Solve the inequality for $y$

$\begin{array} { l }\begin{array} { l }y < 5,& y+3 \geq 0\end{array},\\\begin{array} { l }-\left( y+3 \right) < 8,& y+3 < 0\end{array}\end{array}$

Solve the inequality for $y$

$\begin{array} { l }\begin{array} { l }y < 5,& y \geq -3\end{array},\\\begin{array} { l }-\left( y+3 \right) < 8,& y+3 < 0\end{array}\end{array}$

Solve the inequality for $y$

$\begin{array} { l }\begin{array} { l }y < 5,& y \geq -3\end{array},\\\begin{array} { l }y > -11,& y+3 < 0\end{array}\end{array}$

Solve the inequality for $y$

$\begin{array} { l }\begin{array} { l }y < 5,& y \geq -3\end{array},\\\begin{array} { l }y > -11,& y < -3\end{array}\end{array}$

Find the intersection

$\begin{array} { l }y \in \left[ -3, 5\right\rangle,\\\begin{array} { l }y > -11,& y < -3\end{array}\end{array}$

Find the intersection

$\begin{array} { l }y \in \left[ -3, 5\right\rangle,\\y \in \langle-11, -3\rangle\end{array}$

Find the union

\begin{align*}&y \in \langle-11, 5\rangle\end{align*}

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