Question

Answer 1

\(\Rightarrow\left(x+x+...+x\right)-\left(1+2+...+100\right)=-5150\\ \Rightarrow100x-5050=-5150\\ \Rightarrow100x=-100\\ \Rightarrow x=-1\)

Answer 2

\(\Leftrightarrow100x-\left(1+2+...+100\right)=-5150\\ \Leftrightarrow100x-\dfrac{\left(100+1\right)\left(100-1+1\right)}{2}=-5150\\ \Leftrightarrow100x-5050=-5150\\ \Leftrightarrow100x=-100\\ \Leftrightarrow x=-1\)