Question

решите неравенства даю 30 баллов​

Answer 1

Ответ:

$1)\ \ (2x+1)(1-x)(x-5)\leq 0\ \ \Rightarrow \ \ 2\, (x+0,5)(x-1)(x-5)\geq 0\\\\znaki:\ \ \ ---[-0,5\ ]+++[\ 1\ ]---[\ 5\ ]+++\\\\x\in [\, -0,5\ ;\ 1\ ]\cup [\ 5\ ;+\infty \, )\\\\\\2)\ \ x\, (x+7)(x-4)\leq 0\\\\znaki:\ \ ---[-7\ ]+++[\ 0\ ]---[\ 4\ ]+++\\\\x\in (-\infty \, ;-7\ ]\cup [\ 0\ ;\ 4\ ]$

$3)\ \ 3x^2+5x-8\geq 0\ \ ,\ \ D=121\ ,\ \ x_1=-\dfrac{8}{3}\ ,\ x_2=1\\\\3(x+\frac{8}{3})(x-1)\geq 0\\\\znaki:\ \ \ +++[-\frac{8}{3}\ ]---[\ 1\ ]+++\\\\x\in (-\infty \, ;\ -2\frac{2}{3}\ ]\cup [\ 1\ ;+\infty \, )$

$4)\ \ \dfrac{5x-4}{5-4x}\geq 0\ \ \ \ \Rightarrow \ \ \ \ \ \dfrac{5x-4}{4x-5}\leq 0\ ,\ \ x\ne 1,25\\\\ znaki:\ \ \ +++[\ 0,8\ ]---(\ 1,25\ )+++\\\\x\in [\ 0,8\ ;\ 1,25\ )$