Question

решить
|x+3|+2x$\geq$6

Answer 1

Решение задания прилагаю

Answer 2

Ответ.

$|x+3|+2x\geq 6\\\\|x+3|\geq 6-2x\ \ \ \Rightarrow \ \ \ \left[\begin{array}{l}x+3\geq 6-2x\\x+3\leq 2x-6\end{array}\right\ \ \left[\begin{array}{l}x+2x\geq 6-3\\x-2x\leq -6-3\end{array}\right$

$\left[\begin{array}{l}3x\geq 3\\-x\leq -9\end{array}\right\ \ \left[\begin{array}{l}x\geq 1\\x\geq 9\end{array}\right\ \ \ \ \Rightarrow \ \ \ x\geq 1\\\\\\Otvet:\ \ x\in [\ 1\ ;\ +\infty \, )\ .$

$\star \ \ \ |x|\geq a\ \ \ \Rightarrow \ \ \ \left[\begin{array}{l}x\geq a\\x\leq -a\end{array}\right\ \ \star$