Answer
(a) $0 \gt -2$
(b) $-8 \gt -10$
(c) $-9 \gt -15$
(d) $6 \lt 10$
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:
$\begin{array}{ccc}
&-3 +3 &\gt &-5+3
\\&0 &\gt &-2
\end{array}$
(b) Subtracting 5 from each side of the given inequality:
$\begin{array}{ccc}
& -3-5 &\gt &-5-5
\\&-8 &\gt &-10
\end{array}$
(c) Multiplying 3 to each side of the given inequality:
$\begin{array}{ccc}
&-3(3) &\gt &-5(3)
\\&-9 &\gt &-15
\end{array}$
(d) Multiplying $-2$ to each side of the given inequality:
$\begin{array}{ccc}
&-2(-3) &\lt &-2(-5)
\\&6 &\lt &10
\end{array}$
