# Calculate: 5 * |12-r| > 15

## Expression: $5 \times |12-r| > 15$

Separate the inequality into $2$ possible cases

$\begin{array} { l }\begin{array} { l }5\left( 12-r \right) > 15,& 12-r \geq 0\end{array},\\\begin{array} { l }5 \times \left( -\left( 12-r \right) \right) > 15,& 12-r < 0\end{array}\end{array}$

Solve the inequality for $r$

$\begin{array} { l }\begin{array} { l }r < 9,& 12-r \geq 0\end{array},\\\begin{array} { l }5 \times \left( -\left( 12-r \right) \right) > 15,& 12-r < 0\end{array}\end{array}$

Solve the inequality for $r$

$\begin{array} { l }\begin{array} { l }r < 9,& r \leq 12\end{array},\\\begin{array} { l }5 \times \left( -\left( 12-r \right) \right) > 15,& 12-r < 0\end{array}\end{array}$

Solve the inequality for $r$

$\begin{array} { l }\begin{array} { l }r < 9,& r \leq 12\end{array},\\\begin{array} { l }r > 15,& 12-r < 0\end{array}\end{array}$

Solve the inequality for $r$

$\begin{array} { l }\begin{array} { l }r < 9,& r \leq 12\end{array},\\\begin{array} { l }r > 15,& r > 12\end{array}\end{array}$

Find the intersection

$\begin{array} { l }r \in \langle-\infty, 9\rangle,\\\begin{array} { l }r > 15,& r > 12\end{array}\end{array}$

Find the intersection

$\begin{array} { l }r \in \langle-\infty, 9\rangle,\\r \in \langle15, +\infty\rangle\end{array}$

Find the union

$r \in \langle-\infty, 9\rangle \cup \langle15, +\infty\rangle$

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