a) $(x+\dfrac{1}{3})+(x+\dfrac{1}{6})+(x+\dfrac{1}{18})=\dfrac{15}{9}$
$x+\dfrac{1}{3}+x+\dfrac{1}{6}+x+\dfrac{1}{18}=\dfrac{15}{9}$
$3x+(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{18})=\dfrac{15}{9}$
$3x+(\dfrac{6}{18}+\dfrac{3}{18}+\dfrac{1}{18})=\dfrac{15}{9}$
$3x+\dfrac{5}{9}=\dfrac{15}{9}$
$3x=\dfrac{15}{9}-\dfrac{5}{9}=\dfrac{10}{9}$
$x=\dfrac{10}{9}:3=\dfrac{10}{9}.\dfrac{1}{3}$
$→x=\dfrac{10}{27}$
b) $(x+1)+(x+2)+(x+3)+...+(x+50)=25.52=1300$
$x+1+x+2+x+3+...+x+50=1300$
$50x+(1+2+3+4+...+50)=1300$
$50x+\dfrac{(50+1).50}{2}=1300$
$50x+1275=1300$
$50x=1300-1275=25$
$→x=\dfrac{25}{50}=\dfrac{1}{2}$
