a) $28+2x=35-(-13)$
$⇔ 2x = 35 + 13 - 28$
$⇔ 2x = 20$
$⇔ x = 10 $
b) $2(x+1)^2 = -7 +15$
$⇔ 2(x+1)^2 = 8$
$⇔ (x+1)^2 = 4$
$⇔\left[ \begin{array}{l}x+1=2\\x+1=-2\end{array} \right. $
$⇔ \left[ \begin{array}{l}x=1\\x=-3\end{array} \right. $
c)$ -25-(x+5) = 415+5(x-83)$
$⇔-25 -x - 5 = 415+5x - 415$
$⇔ 6x = -30$
$⇔ x=-5$
d) $|x-2|+(-7)=-3$
$⇔ |x-2| = 4$
$⇔\left[ \begin{array}{l}x-2=4\\x-2=-4\end{array} \right. $
$⇔\left[ \begin{array}{l}x=6\\x=-2\end{array} \right.$
e) $8-|x+2|=5$
$⇔ |x+2| = 3$
$⇔ \left[ \begin{array}{l}x+2=3\\x+2=-3\end{array} \right. $
$⇔\left[ \begin{array}{l}x=1\\x=-5\end{array} \right.$
f) $(x+1)+(x+3)+...+(x+99)=0$
$⇔ 50x + \frac{50.100}{2} = 0 $
$⇔ 50x = -2500$
$⇔ x = -50$
g) $(x-3)+(x-2)+...+10+11 = 11$
$⇔ 3x + (4+5+6+...+10) = 0 $
$ ⇔ 3x = 49 $
$⇔ x= \frac{49}{3}$
