tex]...

zhannaarkadievna @zhannaarkadievna

August 2021 1 9 Report

[tex] \frac{2x - 5}{ |x - 1| } \leqslant 1[/tex]

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xtoto $\frac{2x-5}{|x-1|} \leq 1\\\\
\frac{2x-5}{|x-1|} - 1 \leq 0\\\\
\frac{2x-5-|x-1|}{|x-1|} \leq 0\\\\
 \left \{ {{2x-5-|x-1| \leq 0} \atop {x\neq1}} \right. \\\\
 \left \{ {{|x-1| \geq 2x-5} \atop {x\neq1}} \right. \\\\
 \left \{ {{x-1 \geq 2x-5\ \ \ or\ \ \ x-1 \leq -(2x-5)} \atop {x\neq1}} \right. \\\\
 \left \{ {{4 \geq x\ \ \ or\ \ \ 3x \leq 6} \atop {x\neq1}} \right. \\\\
 \left \{ {{x \leq 4\ \ \ or\ \ \ x \leq 2} \atop {x\neq1}} \right. \\\\
 \left \{ {{x \leq 4} \atop {x\neq1}} \right.$

$x\in(-\infty;\ 1)\cup(1;\ 4]$

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