$\displaystyle 3 - \frac{x}{2} > 7$
is this right?
$\displaystyle \frac{x}{2} > 7 - 3$
$\displaystyle \frac{x}{2} > 4$
$\displaystyle x < 8$
?
No
From $\displaystyle 3 - \frac{x}{2} > 7$
Add $\displaystyle \frac{x}{2}$ to both sides
$\displaystyle 3 > 7 + \frac{x}{2}$
Subtract 7
$\displaystyle 3 - 7 > \frac{x}{2}$
$\displaystyle -4 > \frac{x}{2}$
Multiply by 2 (positive number therefore does not change the sense of the inequality)
$\displaystyle -8 > x$