Question

2)Determine  o conjunto verdade das seguintes inequações:

 

a) 2(1-x) < 2/3 – 2 (2x-2)

 

 

 

b) 1< 2x – 4 ≤ 6

Answer 1

a)
$2(1-x)<\frac{2}{3}-2(2x-2)\\\\2-2x<\frac{2}{3}-4x+4\\\\4x-2x<\frac{2}{3}+4-2\\\\2x<\frac{2}{3}+2\\\\6x<2+6\\\\6x<8\;\;\div(2\\\\\boxed{x<\frac{4}{3}}$

b)
$1<2x-4\leq6\\\\1+4<2x\leq6+4\\\\5<2x\leq10\;\;\div(2\\\\\boxed{\frac{5}{2}<x\leq5}$