Reduce to l form $ ax ^ 2 + bx + c $ in the first member, $ 0 $ in the 2nd member, then use the discussion of the sign of$T = ax^2+ bx+c $ $\Delta = b^2 - 4ac$ ------------------------------- Si $\Delta\lt 0$: $T$ a le sign of $a$ ------------------------------- Si $\Delta = 0$: $T$ has the sign of $a$, if $x$ is not equal to the root $x_0$ $ T = 0 $, if $ x $ is equal to the root $ x_0 $ ------------------------------- If $ \Delta \gt 0 $: $ T = 0 $, if $ x $ is equal to the roots $ x_1 $ or $ x_2 $ $ T $ has the sign of $ a $, if $ x $ is outside the roots $ x_1 $ and $ x_2 $ $ T $ has the sign of $ -a $, if $ x $ is between the roots $ x_1 $ and $ x_2 $ ------------------------------- -------------------------------  

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Solve:

$-x^2 \lt x - 12$
$x^2 \lt 8 - 7x$
$x^2 + 31x \gt -150$
$x^2 -3x \geq -2$
$x^2 + 31x \gt -150$
$5 - 4x \gt x^2$
$4x(x+3) \geq -9$
$5 - 4x \gt x^2$