Question

Calculați: |2x+15| mai mare sau egal cu 13

Answer 1

$|2x+15| \geq 13 \Rightarrow \left\| \begin{array}{c} 2x+15\leq-13 \\ sau \\ 2x+15 \geq 13 \end{array} \right \Rightarrow\left\| \begin{array}{c} 2x\leq-13-15 \\ sau \\ 2x \geq 13 -15 \end{array} \right \Rightarrow$

$\Rightarrow\left\| \begin{array}{c} 2x\leq-28 \\ sau \\ 2x \geq -2\end{array} \right \Rightarrow\left\| \begin{array}{c} x\leq-\dfrac{28}{2} \\ sau \\ x \geq -\dfrac{2}{2}\end{array} \right \Rightarrow\left\| \begin{array}{c} x\leq-14 \\ sau \\ x \geq -1\end{array} \right \Rightarrow \\ \\ \\ \Rightarrow \boxed{x\in \Big(-\infty,-14\Big] \cup \Big[-1,+\infty\Big) }$