Question

(x+1)+(x+2)+(x+3)+.........+(x+9)=54

(x+1)+(x+2)+(x+3)+.........+(x+10)=2010

Answer 1

a) (x + 1) + (x + 2) + (x + 3) + ... + (x + 9)   = 54

(x + x + x + ... + x) + (1 + 2 + 3 + ... + 9) = 54

9x + 45 = 54

9x          = 54 - 45

9x          = 9

  x          = 1

b) (x + 1) + (x + 2) + (x + 3) + ... + (x + 10)   = 2010

     (x + x + x + ... + x) + (1 + 2 + 3 + ... + 10) = 2010

      10x + 55 = 2010

      10x          = 2010 - 55

      10x          = 1955

          x          = 391/2.

Answer 2

1)\(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+....+\left(x+9\right)=54\)

\(\Rightarrow x+1+x+2+x+3+.....+x+9=54\)

\(\Rightarrow\left(x+x+x+....+x\right)+\left(1+2+3+....+9\right)=54\)

\(\Rightarrow9x+45=54\)\(\Rightarrow9x=9\Rightarrow x=1\)

2)\(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+....+\left(x+10\right)=2010\)

\(\Rightarrow x+1+x+2+x+3+.....+x+10=2010\)

\(\Rightarrow\left(x+x+x+....+x\right)+\left(1+2+3+....+10\right)=2010\)

\(\Rightarrow10x+55=2010\Rightarrow10x=1995\Rightarrow x=195,5\)