\(\Leftrightarrow\left\{{}\begin{matrix}x\ge3\\x+12\ge x-3+2x+1+2\sqrt{\left(x-3\right)\left(2x+1\right)}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge3\\7-x\ge\sqrt{2x^2-5x-3}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge3\\7-x\ge0\\\left(7-x\right)^2\ge2x^2-5x-3\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}3\le x\le7\\-x^2+9x-52\le0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}3\le x\le7\\-13\le x\le4\end{matrix}\right.\)
\(\Rightarrow3\le x\le4\)
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