Question

Resolva as inequações: (5x - 10) . (3x - 15) < 0

Answer 1

(5x - 10)(3x - 15) < 0
15x² - 75x - 30x + 150 < 0
15x² - 105x + 150 < 0 
x² - 7x + 10 < 0
x² - 7x + 10 = 0

$\displaystyle \mathsf{\Delta = b^2 - 4.a.c}\\ \displaystyle \mathsf{\Delta = (-7)^2 - 4.(1).(10)}\\ \displaystyle \mathsf{\Delta = 49 - 40}\\ \displaystyle \mathsf{\Delta = 9}$

$\displaystyle \mathsf{x = \frac{-b \: \pm \: \sqrt{\Delta}}{2a}}\\ \\ \displaystyle \mathsf{x = \frac{7 \: \pm 3}{2}}\\ \\ \displaystyle \mathsf{x' = 5}\\ \\ \displaystyle \mathsf{x'' = 2}$

Resposta: $\displaystyle \mathsf{\{x\in R/ \:2\ \textless \ x\ \textless \ 5\}}$