ХЕЕЕЛП МИ 9 класс
60 б

ХЕЕЕЛП МИ 9 класс
60 б

  • 1)\quad (x-3)(x-4)(x-5)\ \textless \ 0\\\\---(3)+++(4)---(5)+++\\\\x\in (-\infty ,3)\cup (4,5)\\\\2)\quad (x^2+2x)(4x-2) \geq 0\\\\2x(x+2)(2x-1) \geq 0\\\\---[-2]+++[0]---[\frac{1}{2}]+++\\\\x\in [-2,0\, ]\cup [\frac{1}{2},+\infty )\\\\3)\quad \frac{x-5}{x+3} \ \textgreater \ 0\qquad +++(-3)---(5)+++\\\\x\in (-\infty ,-3)\cup (5,+\infty )\\\\ 4)\quad \frac{3x+1}{x-2 } \ \textless \ 1\; ,\ \; \frac{3x+1-x+2}{x-2} \ \textless \ 0\; ,\; \; \frac{2x+3}{x-2} \ \textless \ 0\\\\+++(-3/2)---(2)+++\\\\x\in (-\frac{3}{2},2)

    5)\quad \frac{x^2-16}{x+1} \leq 0\; ,\; \; \frac{(x-4)(x+4)}{x+1} \leq 0\\\\---[-4]+++(-1)---[\, 4\, ]+++\\\\x\in (-\infty ,-4\, ]\cup (-1,4\, ]\\\\6)\quad \left \{ {{(x+3)(x-2)\ \textgreater \ 0} \atop {(x+4)(x-3) \leq 0}} \right. \; \left \{ {{x\in (-\infty ,-3)\cup(2,+\infty )} \atop {x\in [-4,3\, ]}} \right. \; x\in [-4,-3)\cup (2,3\, ]\\\\7)\quad \left \{ {{(x-3)(x-1) \geq 0} \atop {x\ \textgreater \ 2}} \right. \; \left \{ {{x\in (-\infty ,1\, ]\cup [\, 3,+\infty )} \atop {x\in (2,+\infty )}} \right. \; x\in [\, 3,+\infty )

    |x|\ \textless \ 4\qquad \to \quad x\in (-4,4)\\\\x\in [\, 3,4)