Question

Tìm x :

e) -12. ( x - 5 ) + 7 . ( 3 - x )=5

g) 30. ( x +2) + 6. ( x - 5 ) - 24x= 102

h) ( x + 1 ) + (x + 2 ) + ... + ( x + 99) =0

Answer 1

- 12 . ( x - 5 ) + 7 . ( 3 - x ) = 5

=> - 12x - 12 . 5 + 7 . 3 - 7x = 5

=> - 12x - 60 + 21 - 7x = 5

=> ( - 12 - 7 )x + ( 60 + 21 ) = 5

=> - 19x + 81 = 5

=> - 19x = - 76

=> x = 4

30 . ( x + 2 ) - 6 . ( x + 5 ) - 24x = 100

=> 30x + 30 . 2 - 6x + 6 . 5 - 24x = 100

=> 30x + 60 - 6x + 30 - 24x = 100

=> 0 . x = 100

=> Không có giá trị x

( x + 1 ) + ( x + 2 ) + . . . + ( x + 99 ) = 0

=> x . 99 + ( 1 + 2 + . . . + 99 ) = 0

=> x . 99 + 4950 = 0

=> x . 99 = - 4950

=> x = - 50

Answer 2

\(\left(x+1\right)+\left(x+2\right)+...+\left(x+99\right)=0\)

\(x+1+x+2+...+x+99=0\)

\(99x+\left(1+2+3+...+98+99\right)=0\)

 \(99x+\frac{\left(99+1\right).99}{2}=0\)

\(99x+4950=0\)

\(99x=-4950\)

\(x=-4950:99=-50\)