Question

Gasiti toate valorile lui x:
$\frac{5}{|2-x|} \geq 1$

Answer 1

[tex] \frac{5}{|2-x|}\geq 1|()^{-1} \Rightarrow \frac{ |2-x| }{5} \leq 1|\cdot 5 \Rightarrow |2-x| \leq 5 \Rightarrow -5 \leq 2-x\leq 5 \\ \\ \[ \left\{ \begin{array}{II} 2-x \geq -5 & & 2-x\leq 5 \end{array} \right. \] $ \ \Rightarrow \[ \left\{ \begin{array}{II} -x \geq -5-2 & & -x\leq 5-2 \end{array} \right. \] $ \ \Rightarrow \[ \left\{ \begin{array}{II} -x \geq -7 & & -x\leq 3 \end{array} \right. \] \end{array} [/tex]

[tex]\Rightarrow \[ \left\{ \begin{array}{II} x \leq 7 & & x \geq -3 \end{array} \right. \] [/tex]

$\RIghtarrow x\in [-3, 7]$