Calculate: |2x-1| >= 7

Expression: $|2x-1| \geq 7$

Separate the inequality into $2$ possible cases

$\begin{array} { l }\begin{array} { l }2x-1 \geq 7,& 2x-1 \geq 0\end{array},\\\begin{array} { l }-\left( 2x-1 \right) \geq 7,& 2x-1 < 0\end{array}\end{array}$

Solve the inequality for $x$

$\begin{array} { l }\begin{array} { l }x \geq 4,& 2x-1 \geq 0\end{array},\\\begin{array} { l }-\left( 2x-1 \right) \geq 7,& 2x-1 < 0\end{array}\end{array}$

Solve the inequality for $x$

$\begin{array} { l }\begin{array} { l }x \geq 4,& x \geq \frac{ 1 }{ 2 }\end{array},\\\begin{array} { l }-\left( 2x-1 \right) \geq 7,& 2x-1 < 0\end{array}\end{array}$

Solve the inequality for $x$

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

Solve the inequality for $x$

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

Find the intersection

$\begin{array} { l }x \in \left[ 4, +\infty\right\rangle,\\\begin{array} { l }x \leq -3,& x < \frac{ 1 }{ 2 }\end{array}\end{array}$

Find the intersection

$\begin{array} { l }x \in \left[ 4, +\infty\right\rangle,\\x \in \left\langle-\infty, -3\right]\end{array}$

Find the union

$x \in \left\langle-\infty, -3\right] \cup \left[ 4, +\infty\right\rangle$