| {x}^(2) + 3x +2 | < 2x + 4 solve the following inequalities

asked Feb 22, 2023 220k views

17 votes

$| {x}^(2) + 3x +2 | < 2x + 4$
solve the following inequalities

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1 vote

$\\ \tt\hookrightarrow |x^2+3x+2|<2x+4$

Either

$\\ \tt\hookrightarrow x^2+3x+2<-2x-4$

$\\ \tt\hookrightarrow x^2+3x+2x<-4-2$

$\\ \tt\hookrightarrow x^2+5x+6<0$

$\\ \tt\hookrightarrow (x+2)(x+3)<0$

$\\ \tt\hookrightarrow x<-2\:or \:x\:-3$

$\\ \tt\hookrightarrow x^2+3x+2<2x+4$

$\\ \tt\hookrightarrow x^2+x-2<0$

$\\ \tt\hookrightarrow x^2+2x-x-2<0$

$\\ \tt\hookrightarrow (x+2)(x-1)<0$

$\\ \tt\hookrightarrow x<-2\:or \:x<1$

$\\ \tt\hookrightarrow x\in (-3,1)$

Vandsh answered Feb 26, 2023

5.4k points

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