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