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[tex] | {x}^{2} + 3x +2 | < 2x + 4[/tex]
solve the following inequalities​

Sagot :

[tex]\\ \tt\hookrightarrow |x^2+3x+2|<2x+4[/tex]

Either

[tex]\\ \tt\hookrightarrow x^2+3x+2<-2x-4[/tex]

[tex]\\ \tt\hookrightarrow x^2+3x+2x<-4-2[/tex]

[tex]\\ \tt\hookrightarrow x^2+5x+6<0[/tex]

[tex]\\ \tt\hookrightarrow (x+2)(x+3)<0[/tex]

[tex]\\ \tt\hookrightarrow x<-2\:or \:x\:-3[/tex]

Or

[tex]\\ \tt\hookrightarrow x^2+3x+2<2x+4[/tex]

[tex]\\ \tt\hookrightarrow x^2+x-2<0[/tex]

[tex]\\ \tt\hookrightarrow x^2+2x-x-2<0[/tex]

[tex]\\ \tt\hookrightarrow (x+2)(x-1)<0[/tex]

[tex]\\ \tt\hookrightarrow x<-2\:or \:x<1[/tex]

So

[tex]\\ \tt\hookrightarrow x\in (-3,1)[/tex]

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