Answer
(a) $7 \gt 0$
(b) $-1 \gt -8$
(c) $12 \gt -9$
(d) $-8 \lt 6$
Work Step by Step
RECALL:
(1) When a real number is added or subtracted to each side of an inequality, the sense/direction of the inequality is not affected.
(2) When a negative number is multiplied to each side of an inequality, the sense/direction of the inequality will change.
Use the rules above to obtain:
(a) Adding 3 to each side of the given inequality:
$\begin{array}{ccc}
&3 +4 &\gt &3+(-3)
\\&7 &\gt &0
\end{array}$
(b) Subtracting 5 from each side of the given inequality:
$\begin{array}{ccc}
&4 -5 &\gt &-3-5
\\&-1&\gt &-8
\end{array}$
(c) Multiplying 3 to each side of the given inequality:
$\begin{array}{ccc}
&3(4) &\gt &3(-3)
\\&12 &\gt &-9
\end{array}$
(d) Multiplying $-2$ to each side of the given inequality:
$\begin{array}{ccc}
&-2(4) &\lt &-2(-3)
\\&-8 &\lt &6
\end{array}$