a)2(1−x)−3(x−2)<8
−5x+8<8
−5x+8−8<8−8−5x<0
[tex] \frac{-5x}{-5} \ \textless \ \frac{0}{-5} [/tex]
x>0
6x-3<17-(x-5)
6x−3<−x+22
6x−3+x<−x+22+x
7x−3<22
7x−3+3<22+37x<25
[tex] \frac{7x}{7} \ \textless \ \frac{25}{7} [/tex]
x<[tex] \frac{25}{7} [/tex]
b) 3(x+8)>4(7-x)
3x+24>−4x+28
3x+24+4x>−4x+28+4x7x+24>28
7x+24−24>28−247x>4
[tex] \frac{7x}{7} \ \textgreater \ \frac{4}{7} [/tex]
x>[tex] \frac{4}{7} [/tex]
(x+2)(x-5)>(x+3(x-4)
x2−3x−10>4x−12
x2−3x−10=4x−12x2−3x−10−(4x−12)=4x−12−(4x−12)
x2−7x+2=0
x=[tex] \frac{-b±√b2−4ac}{2a} [/tex]
x=[tex] \frac{-(-7)±√(-7)2-4(1)(2)}{2(1)} [/tex]
x=[tex] \frac{7±√41}{2} [/tex]
x=[tex] \frac{7}{2} + \frac{1}{2} \sqrt{41} [/tex]
