Solve the inequality involving absolute value.
|x−2|+4≥10
Enter the exact answer in interval notation.
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Accepted Solution
A:
$|x-2| \geq 10-4$
$|x-2| \geq 6$
$\begin{array} { l }\begin{array} { l }x-2 \geq 6,& x-2 \geq 0\end{array},\\\begin{array} { l }-\left( x-2 \right) \geq 6,& x-2 < 0\end{array}\end{array}$
$\begin{array} { l }\begin{array} { l }x \geq 8,& x-2 \geq 0\end{array},\\\begin{array} { l }-\left( x-2 \right) \geq 6,& x-2 < 0\end{array}\end{array}$
$\begin{array} { l }\begin{array} { l }x \geq 8,& x \geq 2\end{array},\\\begin{array} { l }-\left( x-2 \right) \geq 6,& x-2 < 0\end{array}\end{array}$
$\begin{array} { l }\begin{array} { l }x \geq 8,& x \geq 2\end{array},\\\begin{array} { l }x \leq -4,& x-2 < 0\end{array}\end{array}$
$\begin{array} { l }\begin{array} { l }x \geq 8,& x \geq 2\end{array},\\\begin{array} { l }x \leq -4,& x < 2\end{array}\end{array}$
$\begin{array} { l }x \in \left[ 8, +\infty\right\rangle,\\\begin{array} { l }x \leq -4,& x < 2\end{array}\end{array}$