3) 2х²-7х-4≤0
2х²-7х-4=0
D = (-7)² - 4 * 2 * (-4) = 49 + 32 = 81 = 9²
![x_{1} = \frac{7+\sqrt{81} }{2*2} = \frac{7+9}{4} = \frac{16}{4} = 4 x_{1} = \frac{7+\sqrt{81} }{2*2} = \frac{7+9}{4} = \frac{16}{4} = 4](https://tex.z-dn.net/?f=x_%7B1%7D%20%3D%20%5Cfrac%7B7%2B%5Csqrt%7B81%7D%20%7D%7B2%2A2%7D%20%3D%20%20%5Cfrac%7B7%2B9%7D%7B4%7D%20%3D%20%5Cfrac%7B16%7D%7B4%7D%20%3D%204)
![\\x_{2} = \frac{7 - \sqrt{81} }{2*2} = \frac{7 - 9 }{4} = \frac{ -2 }{4} = - \frac{ 1}{2} = -0,5 \\x_{2} = \frac{7 - \sqrt{81} }{2*2} = \frac{7 - 9 }{4} = \frac{ -2 }{4} = - \frac{ 1}{2} = -0,5](https://tex.z-dn.net/?f=%5C%5Cx_%7B2%7D%20%3D%20%5Cfrac%7B7%20-%20%5Csqrt%7B81%7D%20%7D%7B2%2A2%7D%20%3D%20%20%5Cfrac%7B7%20-%209%20%7D%7B4%7D%20%3D%20%5Cfrac%7B%20-2%20%7D%7B4%7D%20%3D%20-%20%5Cfrac%7B%201%7D%7B2%7D%20%3D%20-0%2C5)
х∈[-0,5 ; 4]
т.к. -0,5 не является целым числом => целыми решениями неравенств являются:
х∈[0;4]
Ответ: х∈[0;4]
4) ![\left \{ {{8x -2<x-1} \atop {2x^{2}}-x-1\leq 0} \right. \left \{ {{8x -2<x-1} \atop {2x^{2}}-x-1\leq 0} \right.](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7B8x%20-2%3Cx-1%7D%20%5Catop%20%7B2x%5E%7B2%7D%7D-x-1%5Cleq%200%7D%20%5Cright.)
![\left \{ {{7x < 1} \atop {2x^{2}}-x-1\leq 0} \right. \left \{ {{7x < 1} \atop {2x^{2}}-x-1\leq 0} \right.](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7B7x%20%3C%201%7D%20%5Catop%20%7B2x%5E%7B2%7D%7D-x-1%5Cleq%200%7D%20%5Cright.)
2х²-х-1=0
D = (-1)² - 4*2*(-1) = 1 + 8 = 9 = 3²
![x_{1} =\frac{1 + \sqrt{9} }{2*2} = \frac{1+3}{4} = \frac{4}{4} = 1 x_{1} =\frac{1 + \sqrt{9} }{2*2} = \frac{1+3}{4} = \frac{4}{4} = 1](https://tex.z-dn.net/?f=x_%7B1%7D%20%3D%5Cfrac%7B1%20%2B%20%5Csqrt%7B9%7D%20%7D%7B2%2A2%7D%20%3D%20%5Cfrac%7B1%2B3%7D%7B4%7D%20%3D%20%5Cfrac%7B4%7D%7B4%7D%20%3D%201)
![x_{2} =\frac{1 - \sqrt{9} }{2*2} = \frac{1-3}{4} = \frac{-2}{4} = -0,5 x_{2} =\frac{1 - \sqrt{9} }{2*2} = \frac{1-3}{4} = \frac{-2}{4} = -0,5](https://tex.z-dn.net/?f=x_%7B2%7D%20%3D%5Cfrac%7B1%20-%20%5Csqrt%7B9%7D%20%7D%7B2%2A2%7D%20%3D%20%5Cfrac%7B1-3%7D%7B4%7D%20%3D%20%5Cfrac%7B-2%7D%7B4%7D%20%3D%20-0%2C5)
х∈[-0,5 ; 1]
![\left \{ {x < \frac{1}{7} } \atop {\left[\begin{array}{ccc}x\geq -0,5\\x\leq 1\\\end{array} \left \{ {x < \frac{1}{7} } \atop {\left[\begin{array}{ccc}x\geq -0,5\\x\leq 1\\\end{array}](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7Bx%20%3C%20%5Cfrac%7B1%7D%7B7%7D%20%7D%20%5Catop%20%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5Cgeq%20%20-0%2C5%5C%5Cx%5Cleq%20%201%5C%5C%5Cend%7Barray%7D)
х∈[-0,5 ;
)
Ответ: х∈[
)