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
Since $2x+1\lt 2$, then;
(a) Adding $3$ to each side of the given inequality;
$$3+2x+1\lt 2+3\Longrightarrow2x+4\lt 5$$
(b) Subtracting $5$ from each side of the given inequality;
$$2x+1-5\lt 2-5\Longrightarrow 2x-4\lt -3$$
(c) Multiplying each side of the given inequality by $3$;
$$3\times(2x+1)\lt 2\times3\Longrightarrow 6x+3\lt 6$$
(d) Multiplying each side of the given inequality by -$ 2$;
$$-2\times(2x+1)\gt 2\times(-2)\Longrightarrow -4x-2\gt -4\\
\text{(The inequality symbol will change since a negative number was multiplied to both sides.)}$$
