(x+1)+(x+3)+...+(x+99)=1000
=>50x+1+3+...+99=1000
=>50x+\(\dfrac{\left(99-1\right):2+1\cdot\left(1+99\right)}{2}\)=1000
=>50x+2500=1000
=>50x=1000-2500=-1500
=>x=-1500:50=-30.
\(\left(x+1\right)+\left(x+3\right)+\left(x+5\right)+...+\left(x+99\right)=1000\)
\(\left(x+x+x+...+x\right)+\left(1+3+5+7+9+...+99\right)\)
\(\left(x.50\right)+2500\)=1000
\(x.50=1000-2500\)
\(x.50=-1500\)
\(x=-1500:50=-30\)