\(\left(x-1\right)+\left(x-2\right)+\left(x-3\right)+...+\left(x-10\right)=15\times25\times4+75\)
\(x-1+x-2+x-3+...+x-10=15\times\left(25\times4\right)+75\)
\(\left(x+x+x+...+x\right)-\left(1+2+3+...+10\right)=15\times100+75\)
\(10x-55=1500+75\)
\(10x-55=1575\)
\(10x=1575+55\)
\(10x=1630\)
\(x=1630:10\)
\(x=163\)