Question #319102

25/x<10


1
Expert's answer
2022-03-31T02:24:13-0400

25x<102510xx<0x2.5x>0[{x2.5>0x>0{x2.5<0x<0[x>2.5x<0x(,0)(2.5,+)\frac{25}{x}<10\Leftrightarrow \frac{25-10x}{x}<0\Leftrightarrow \frac{x-2.5}{x}>0\Leftrightarrow \left[ \begin{array}{c} \left\{ \begin{array}{c} x-2.5>0\\ x>0\\\end{array} \right.\\ \left\{ \begin{array}{c} x-2.5<0\\ x<0\\\end{array} \right.\\\end{array} \right. \Leftrightarrow \left[ \begin{array}{c} x>2.5\\ x<0\\\end{array} \right. \Leftrightarrow x\in \left( -\infty ,0 \right) \cup \left( 2.5,+\infty \right)


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