Question

Please solve thisa1" title=" |x ^{2} + 3x - 1 | < 3" alt=" |x ^{2} + 3x - 1 | < 3" align="absmiddle" class="latex-formula">

Answer 1

$\bf |x^2+3x-1|\ \textless \ 3\implies \begin{cases} +(x^2+3x-1)\ \textless \ 3\\\\ -(x^2+3x-1)\ \textless \ 3 \end{cases}\\\\ -------------------------------\\\\ x^2+3x-1\ \textless \ 3\implies x^2+3x-4\ \textless \ 0\implies (x+4)(x-1)\ \textless \ 0 \\\\\\ x\ \textless \ \begin{cases} -4\\ 1 \end{cases}\\\\ -------------------------------\\\\ -(x^2+3x-1)\ \textless \ 3\implies x^2+3x-1\boxed{\ \textgreater \ }-3 \\\\\\ x^2+3+2\ \textgreater \ 0\implies (x+2)(x+1)\ \textgreater \ 0\implies x\ \textgreater \ \begin{cases} -2\\ -1 \end{cases}$