Question

Rezolvati in R inecuatia 4x-8/3x+9≤0 si 3+1/2x-8 < 1.

Answer 1

$\frac{4x-8}{3x+9} \leq 0$
$\left \{ {{4x-8 \leq 0} \atop {3x+9\ \textgreater \ 0}} \right.$
$\left \{ {{4x-8 \geq 0} \atop {3x+9\ \textless \ 0}} \right.$
$\left \{ {{x \leq 2} \atop {x\ \textgreater \ -3}} \right.$
$\left \{ {{x \geq 2} \atop {x\ \textless \ -3}} \right.$
x∈(-3, 2]
x∈∅

$\frac{3+1}{2x-8}\ \textless \ 1$
$\frac{4}{2(x-4)}\ \textless \ 1$
$\frac{2}{x-4}\ \textless \ 1$
$\frac{2}{x-4}-1\ \textless \ 0$
$\frac{2-(x-4)}{x-4}\ \textless \ 0$
$\frac{2-x+4}{x-4}\ \textless \ 0$
$\frac{6-x}{x-4}\ \textless \ 0$
$\left \{ {{6-x\ \textless \ 0} \atop {x-4\ \textgreater \ 0}} \right.$
$\left \{ {{6-x\ \textgreater \ 0} \atop {x-4\ \textless \ 0}} \right.$
$\left \{ {{x\ \textgreater \ 6} \atop {x\ \textgreater \ 4}} \right.$
$\left \{ {{x\ \textless \ 6} \atop {x\ \textless \ 4}} \right.$
x∈(6, +∞)
x∈(-∞, 4)
x∈(-∞, 4)∪(6, +∞)