Answer
(a) $5 \gt 4$
(b) $-3 \gt -4$
(c) $6 \lt 3$
(d) $-4 \lt -2$
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:
$\begin{array}{ccc}
&2 +3 &\gt &1+3
\\&5 &\gt &4
\end{array}$
(b) Subtracting 5 from each side of the given inequality:
$\begin{array}{ccc}
&2 -5 &\gt &1-5
\\&-3 &\gt &-4
\end{array}$
(c) Multiplying 3 to each side of the given inequality:
$\begin{array}{ccc}
&3(2) &\gt &3(1)
\\&6 &\gt &3
\end{array}$
(d) Multiplying $-2$ to each side of the given inequality:
$\begin{array}{ccc}
&-2(2) &\lt &-2(1)
\\&-4 &\lt &-2
\end{array}$
