\(\left(x+1\right)+\left(x-2\right)+\left(x+3\right)+\left(x-4\right)...\left(x-50=-175\right)\)
\(\Rightarrow x+1+x-2+x+3+x-4+...+x-50=-175\)
\(\Rightarrow\left(x+x+...+x\right)+\left(1-2+3-4+...-50\right)=-175\)
\(\Rightarrow50x+\left(1-2\right)+\left(3-4\right)+...+\left(49-50\right)=-175\)
\(\Rightarrow50x+\left(-1\right)+\left(-1\right)+...+\left(-1\right)=-175\)
\(\Rightarrow50x+\left(-1\right)50=-175\)
\(\Rightarrow50x+\left(-50\right)=-175\)
\(\Rightarrow50x=-175+50=-125\)
\(\Rightarrow x=-125\div50=\frac{-5}{2}\)
(x+1)+(x-2)+(x+3)+(x-4)+...+(x-50)=-175
x+1+x-2+x+3+x-4+...+x-50=-175
50x+(1-2+3-4+...+49-50)=-175
50x-25=-175
50x=-150
x=-3
