Question

e=" | {x}^{2} + 3x +2 | < 2x + 4" alt=" | {x}^{2} + 3x +2 | < 2x + 4" align="absmiddle" class="latex-formula">
solve the following inequalities​

Answer 1

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

Either

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

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

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

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

$\\ \tt\hookrightarrow x$

Or

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

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

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

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

$\\ \tt\hookrightarrow x$

So

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