Answer
$\text{(a)}\quad$ $4-2x\gt 8$
$\text{(b)}\quad$ $-4-2x\gt0$
$\text{(c)}\quad$ $3-6x\gt 15$
$\text{(d)}\quad$ $-2+4x\lt -10$
Work Step by Step
The given inequality is
$\Rightarrow 1-2x\gt 5$
(a) Add $3$ to each side.
$\Rightarrow 1-2x+3\gt 5+3$
Simplify.
$\Rightarrow 4-2x\gt 8$
(b) Subtract $5$ from each side.
$\Rightarrow 1-2x-5\gt 5-5$
Simplify.
$\Rightarrow -4-2x\gt0$
(c) Multiply each side by $3$.
$\Rightarrow 3\cdot (1-2x)\gt 3\cdot (5)$
Use distributive property.
$\Rightarrow 3-6x\gt 15$.
(d) Multiply each side by $-2$ and change the direction of the inequality.
$\Rightarrow -2\cdot (1-2x)\lt -2\cdot (5)$
Use distributive property.
$\Rightarrow -2+4x\lt -10$.
