Answer
$\text{(a)}\quad$ $2x+4\lt 5$.
$\text{(b)}\quad$ $2x-4\lt-3$.
$\text{(c)}\quad$ $ 6x+3\lt 6$.
$\text{(d)}\quad$ $-4x-2\gt -4$.
Work Step by Step
The given inequality is
$\Rightarrow 2x+1\lt 2$
(a) Add $3$ to each side.
$\Rightarrow 2x+1+3\lt 2+3$
Simplify.
$\Rightarrow 2x+4\lt 5$
(b) Subtract $5$ from each side.
$\Rightarrow 2x+1-5\lt 2-5$
Simplify.
$\Rightarrow 2x-4\lt-3$
(c) Multiply each side by $3$.
$\Rightarrow 3\cdot (2x+1)\lt 3\cdot (2)$
Use distributive property.
$\Rightarrow 6x+3\lt 6$.
(d) Multiply each side by $-2$ and change the direction of the inequality.
$\Rightarrow -2\cdot (2x+1)\gt -2\cdot (2)$
Use distributive property.
$\Rightarrow -4x-2\gt -4$.
