Question

Rezolvati in R sistemul de inecuatii:
{3-4x>5
{6+9x<=1

Answer 1

$3-4x>5 => -4x>2 => x< \frac{2}{-4} <=> x< -\frac{1}{2}$ =>  x∈(-∞;$-\frac{1}{2}$)

$6+9x \leq 1 => 9x \leq -5 => x \leq -\frac{5}{9}$ => x∈(-∞;$- \frac{5}{9}$]

Solutia sistemului este (-∞;$-\frac{1}{2}$) ∩ (-∞;$- \frac{5}{9}$] = (-∞;$-\frac{1}{2}$).

Answer 2

$\left \{ {{3-4x>5} \atop {6+9x\leq1 }} \right.$⇔$\left \{ {{-4x>2} \atop {9x \leq -5}} \right.$⇔$\left \{ {{x< \frac{2}{-4} } \atop {x \leq \frac{-5}{9} }} \right.$⇔$\left \{ {{x< \frac{1}{-2} } \atop {x\leq \frac{-5}{9} }} \right.$
$s=(-infinit; \frac{-5}{9} ]$.