$ T = a x + b $ ------------------------------- If $ a \lt 0 $: $ T \lt 0 $ for $ x \gt \frac {-b} {a} $ $ T \gt 0 $ for $ x \lt \frac {-b} {a} $ ------------------------------- If $ a \gt 0 $ :: $ T \gt 0 $ for $ x \gt \frac {-b} {a} $ $ T \lt 0 $ for $ x \lt \frac {-b} {a} $ ------------------------------- If $ a = 0 $ :: $ T $ has the sign of $ b $ -------------------------------

Got it !

$\LARGE T \lt 0$      When ??

$\LARGE T = -3x + 7$	$\LARGE T\lt 0$ if $\LARGE x\gt \frac{7}{3}$
$\LARGE T = x - 3$	$\LARGE T\lt 0$ if $\LARGE x\lt3$
$\LARGE T = 9x -6$	$\LARGE T\lt 0$ if $\LARGE x\lt \frac{2}{3}$

Answer

Sign of $\LARGE T = -2x+12$ for $\LARGE x=6$	$\LARGE T = 0$
$\LARGE T = x-5\gt 0$ for $\LARGE x\gt ?$	$\LARGE x\gt 5$
$\LARGE -3x \gt 3$ for $\LARGE x ?$	$\LARGE x \lt -1$
$\LARGE 0x -1 \gt 3$ for $\LARGE x ?$	never
$\LARGE -4 \leq 0x$ for $\LARGE x ?$	always