# Evaluate: |2x-3| > 5

## Expression: $|2x-3| > 5$

Separate the inequality into $2$ possible cases

$\begin{array} { l }\begin{array} { l }2x-3 > 5,& 2x-3 \geq 0\end{array},\\\begin{array} { l }-\left( 2x-3 \right) > 5,& 2x-3 < 0\end{array}\end{array}$

Solve the inequality for $x$

$\begin{array} { l }\begin{array} { l }x > 4,& 2x-3 \geq 0\end{array},\\\begin{array} { l }-\left( 2x-3 \right) > 5,& 2x-3 < 0\end{array}\end{array}$

Solve the inequality for $x$

$\begin{array} { l }\begin{array} { l }x > 4,& x \geq \frac{ 3 }{ 2 }\end{array},\\\begin{array} { l }-\left( 2x-3 \right) > 5,& 2x-3 < 0\end{array}\end{array}$

Solve the inequality for $x$

$\begin{array} { l }\begin{array} { l }x > 4,& x \geq \frac{ 3 }{ 2 }\end{array},\\\begin{array} { l }x < -1,& 2x-3 < 0\end{array}\end{array}$

Solve the inequality for $x$

$\begin{array} { l }\begin{array} { l }x > 4,& x \geq \frac{ 3 }{ 2 }\end{array},\\\begin{array} { l }x < -1,& x < \frac{ 3 }{ 2 }\end{array}\end{array}$

Find the intersection

$\begin{array} { l }x \in \langle4, +\infty\rangle,\\\begin{array} { l }x < -1,& x < \frac{ 3 }{ 2 }\end{array}\end{array}$

Find the intersection

$\begin{array} { l }x \in \langle4, +\infty\rangle,\\x \in \langle-\infty, -1\rangle\end{array}$

Find the union

$x \in \langle-\infty, -1\rangle \cup \langle4, +\infty\rangle$

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