Question

Розв'язати нерівність
(х-2)*(х+2)-х менше х^2-5х+8
(3х+5)/2-2більше рівне 2х

Answer 1

$\displaystyle \tt (x-2)(x+2)-2<x^2-5x+8\\\displaystyle \tt x^2-4-x<x^2-5x+8\\\displaystyle \tt -4-x<-5x+8\\\displaystyle \tt -x+5x<8+4\\\displaystyle \tt 4x<12\\\displaystyle \tt x<\frac{12}{4}\\\displaystyle \tt x<3\\\displaystyle \tt \boxed{\bold{x\in (-\infty; \: 3)}}$

$\displaystyle \tt \frac{3x+5}{2}-2\geq 2x \: \: \: \: \: | \cdot2\\\displaystyle \tt 3x+5-4\geq 4x\\\displaystyle \tt 3x+1\geq 4x\\\displaystyle \tt 3x-4x\geq -1\\\displaystyle \tt -x\geq -1\\\displaystyle \tt x\leq 1\\\displaystyle \tt \boxed{\bold{x\in (-\infty; \: 1]}}$