Question

помогите решить неравенство [3-5x]≤ 2

Answer 1

$|3-5x| \leq 2$

1 случай. 
$\left \{ {{\big{3-5x \geq 0} } \atop {\big{3-5x \leq 2}}} \right. ~~~~~ \left \{ {{\big{5x \leq 3} } \atop {\big{5x \geq 1}}} \right.~~~~~\left \{ {{\big{x \leq 0,6} } \atop {\big{x \geq 0,2}}} \right.~~~=\ \textgreater \ x\in[0,2;~0,6]$

2 случай.
$\left \{ {{\big{3-5x \leq 0}} \atop {\big{-3+5x \leq 2}}} \right. ~~~~ \left \{ {{\big{5x\ \geq \ 3}} \atop {\big{5x \leq 5}}} \right. ~~~~ \left \{ {{\big{x\ \geq \ 0,6}} \atop {\big{x \leq 1}}} \right. ~~~~x\in[0,6;~1]$

Ответ: $x\in[0,2;~1]$