Answer
a. $ 4-2x\gt 8$
b. $ -4-2x\gt 0$
c. $3-6x\gt 15$
d. $-2+4x\lt -10$
Work Step by Step
Since $1-2x\gt 5$, then;
(a) Adding $3$ to each side of the given inequality;
$$3+1-2x\gt 5+3\Longrightarrow 4-2x\gt 8$$
(b) Subtracting $5$ from each side of the given inequality;
$$1-2x-5\gt 5-5\Longrightarrow -4-2x\gt 0$$
(c) Multiplying each side of the given inequality by $3$;
$$3\times(1-2x)\gt 3\times5\Longrightarrow 3-6x\gt 15$$
(d) Multiplying each side of the given inequality by $- 2$;
$$-2\times(1-2x)\lt 5\times(-2)\Longrightarrow -2+4x\lt -10.\\
\text{(The inequality symbol will change since a negative number was multiplied to both sides.)}$$
