Answer
(a) $4-2x \gt 8$
(b) $-2x-4 \gt 0$
(c) $3-6x\gt 15$
(d) $-2+4x \lt -10$
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:
$\begin{array}{ccc}
&1-2x+3 &\gt &5+3
\\&4-2x &\gt &8
\end{array}$
(b) Subtracting 5 from each side of the given inequality:
$\begin{array}{ccc}
&1-2x-5&\gt &5-5
\\&-2x-4 &\gt &0
\end{array}$
(c) Multiplying 3 to each side of the given inequality:
$\begin{array}{ccc}
&3(1-2x) &\gt &3(5)
\\&3-6x &\gt &15
\\
\end{array}$
(d) Multiplying $-2$ to each side of the given inequality:
$\begin{array}{ccc}
&-2(1-2x) &\lt &-2(5)
\\&-2-(-4x) &\lt &-10
\\&-2+4x &\lt -10
\end{array}$