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

User Rafaelpadu
by
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1 Answer

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

Or


\\ \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

So


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

User Vandsh
by
7.1k points

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