\(\left(x+9\right)+\left(x-8\right)+\left(x+7\right)+\left(x-6\right)+\left(x+5\right)+\left(x-4\right)+\left(x+3\right)+\left(x-2\right)+\left(x+1\right)=95.9\\ =>x+9+x-8+x+7+x-6+x+5+x-4+x+3+x-2+x+1=855\\ =>\left(x+x+x+x+x+x+x+x+x\right)+\left(9-8+7-6+5-4+3-2+1\right)=855\\ =>9x+5=855\\ =>9x=855-5\\ =>9x=850\\ =>x=\dfrac{850}{9}\)
\(\left(x+9\right)+\left(x-8\right)+...+\left(x-2\right)+\left(x+1\right)\)
\(=x+9+x-8+...+x-2+x+1\)
\(=\left(x+9+x-8\right)+...+\left(x+5\right)+...+\left(x-2+x+1\right)\)
(Ta gộp 4 số vào 1 tổng, riêng (x+5) là ta giữ nguyên)
\(=\left(2x-1\right)+...+\left(x+5\right)+...+\left(2x-1\right)\)
\(=4\left(2x-1\right)+\left(x+5\right)\)
\(=8x-4+x-5\)
\(=9x-9\) (1)
Từ bài toán trên, ta có:
\(\left(x+9\right)+\left(x-8\right)+...+\left(x-2\right)+\left(x+1\right)=95,9\)
Từ (1)
\(\Leftrightarrow9x-9=95,9\)
\(9x=95,9-9\)
\(x=86,9:9\)
\(x=9,6\left(5\right)\)
