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