0\; \; \; \to \; \; \; x\in R\\\\x^2-4>0\; \; ,\; \; (x-2)(x+2)>0\; \; \to \; \; x\in (-\infty ,-2)\cup (2,+\infty )\\\\x^2-4<0\; \; ,\; \; (x-2)(x+2)<0\; \; \to\; \; x\in (-2,2)\\\\x^2+4<0\; \; \; \to \; \; \; x\in \varnothing" alt="1)\; \; x^2+4>0\; \; \; \to \; \; \; x\in R\\\\x^2-4>0\; \; ,\; \; (x-2)(x+2)>0\; \; \to \; \; x\in (-\infty ,-2)\cup (2,+\infty )\\\\x^2-4<0\; \; ,\; \; (x-2)(x+2)<0\; \; \to\; \; x\in (-2,2)\\\\x^2+4<0\; \; \; \to \; \; \; x\in \varnothing" align="absmiddle" class="latex-formula">
![2)\; \; (4-x)(3x-1)(x+8)\leq 0\; \; \; \to \; \; \; (x-4)(3x-1)(x+8)\geq 0\\\\znaki:\; \; ---(-8)+++(\frac{1}{3})---(4)+++\\\\x\in (-8,\frac{1}{3})\cup (4,+\infty )\\\\\\3)\; \; 2x^2+5x+2\geq 0\\\\D=9\; ,\; \; x_1=-2\; ,\; x_2=-\frac{1}{2}\; \; \; \to \; \; \; 2(x+2)(x+\frac{1}{2})\geq 0\\\\znaki:\; \; +++[-2\, ]---[-\frac{1}{2}\, ]+++\\\\x\in (-\infty ,-2\, ]\cup [-\frac{1}{2},+\infty )\\\\\\3x+9<0\; \; \to \; \; 3x<9\; \; \to \; \; x<3\; \; ,\; \; x\in (-\infty ,3)](https://tex.z-dn.net/?f=2%29%5C%3B%20%5C%3B%20%284-x%29%283x-1%29%28x%2B8%29%5Cleq%200%5C%3B%20%5C%3B%20%5C%3B%20%5Cto%20%5C%3B%20%5C%3B%20%5C%3B%20%28x-4%29%283x-1%29%28x%2B8%29%5Cgeq%200%5C%5C%5C%5Cznaki%3A%5C%3B%20%5C%3B%20---%28-8%29%2B%2B%2B%28%5Cfrac%7B1%7D%7B3%7D%29---%284%29%2B%2B%2B%5C%5C%5C%5Cx%5Cin%20%28-8%2C%5Cfrac%7B1%7D%7B3%7D%29%5Ccup%20%284%2C%2B%5Cinfty%20%29%5C%5C%5C%5C%5C%5C3%29%5C%3B%20%5C%3B%202x%5E2%2B5x%2B2%5Cgeq%200%5C%5C%5C%5CD%3D9%5C%3B%20%2C%5C%3B%20%5C%3B%20x_1%3D-2%5C%3B%20%2C%5C%3B%20x_2%3D-%5Cfrac%7B1%7D%7B2%7D%5C%3B%20%5C%3B%20%5C%3B%20%5Cto%20%5C%3B%20%5C%3B%20%5C%3B%202%28x%2B2%29%28x%2B%5Cfrac%7B1%7D%7B2%7D%29%5Cgeq%200%5C%5C%5C%5Cznaki%3A%5C%3B%20%5C%3B%20%2B%2B%2B%5B-2%5C%2C%20%5D---%5B-%5Cfrac%7B1%7D%7B2%7D%5C%2C%20%5D%2B%2B%2B%5C%5C%5C%5Cx%5Cin%20%28-%5Cinfty%20%2C-2%5C%2C%20%5D%5Ccup%20%5B-%5Cfrac%7B1%7D%7B2%7D%2C%2B%5Cinfty%20%29%5C%5C%5C%5C%5C%5C3x%2B9%3C0%5C%3B%20%5C%3B%20%5Cto%20%5C%3B%20%5C%3B%203x%3C9%5C%3B%20%5C%3B%20%5Cto%20%5C%3B%20%5C%3B%20x%3C3%5C%3B%20%5C%3B%20%2C%5C%3B%20%5C%3B%20x%5Cin%20%28-%5Cinfty%20%2C3%29 "2)\; \; (4-x)(3x-1)(x+8)\leq 0\; \; \; \to \; \; \; (x-4)(3x-1)(x+8)\geq 0\\\\znaki:\; \; ---(-8)+++(\frac{1}{3})---(4)+++\\\\x\in (-8,\frac{1}{3})\cup (4,+\infty )\\\\\\3)\; \; 2x^2+5x+2\geq 0\\\\D=9\; ,\; \; x_1=-2\; ,\; x_2=-\frac{1}{2}\; \; \; \to \; \; \; 2(x+2)(x+\frac{1}{2})\geq 0\\\\znaki:\; \; +++[-2\, ]---[-\frac{1}{2}\, ]+++\\\\x\in (-\infty ,-2\, ]\cup [-\frac{1}{2},+\infty )\\\\\\3x+9<0\; \; \to \; \; 3x<9\; \; \to \; \; x<3\; \; ,\; \; x\in (-\infty ,3)")
![\left\{\begin{array}{l}2x^2+5x+2\geq 0\\3x+9<0\end{array}\right\; \; \left\{\begin{array}{l}x\in (-\infty ,-2\, ]\cup [-\frac{1}{2},+\infty )\\x\in (-\infty ,3)\end{array}\right\; \; \Rightarrow \\\\\\x\in (-\infty ;-2\, ]\cup [-\frac{1}{2}\, ;\, 3)](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7D2x%5E2%2B5x%2B2%5Cgeq%200%5C%5C3x%2B9%3C0%5Cend%7Barray%7D%5Cright%5C%3B%20%5C%3B%20%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7Dx%5Cin%20%28-%5Cinfty%20%2C-2%5C%2C%20%5D%5Ccup%20%5B-%5Cfrac%7B1%7D%7B2%7D%2C%2B%5Cinfty%20%29%5C%5Cx%5Cin%20%28-%5Cinfty%20%2C3%29%5Cend%7Barray%7D%5Cright%5C%3B%20%5C%3B%20%5CRightarrow%20%5C%5C%5C%5C%5C%5Cx%5Cin%20%28-%5Cinfty%20%3B-2%5C%2C%20%5D%5Ccup%20%5B-%5Cfrac%7B1%7D%7B2%7D%5C%2C%20%3B%5C%2C%203%29 "\left\{\begin{array}{l}2x^2+5x+2\geq 0\\3x+9<0\end{array}\right\; \; \left\{\begin{array}{l}x\in (-\infty ,-2\, ]\cup [-\frac{1}{2},+\infty )\\x\in (-\infty ,3)\end{array}\right\; \; \Rightarrow \\\\\\x\in (-\infty ;-2\, ]\cup [-\frac{1}{2}\, ;\, 3)")