The sum of 5 consecutive integers is 270

The 5 (FIVE) consecutive integers are:  52, 53, 54, 55, and 56 .

The expression is written as:

 x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 270 ;

  in which the 5 (FIVE) consecutive integers are:

      x, (x + 1), (x + 2), (x + 3), (x + 4) .

   To find the 5 (FIVE) consecutive integers, we solve for "x" , and the plug in the the value of "x" for the expressions of the other integers.

We have:

  x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 270 ;

Rewrite as:

        x + x + 1 + x + 2 + x + 3 + x + 4 = 270 ;

 Combine the "like terms" on the "left-hand side" of the equation:

       x + x + x + x + x = 1x + 1x + 1x + 1x = 1x = 5x ;

      1 + 2 + 3 + 4 = 10 ;

 →  5x + 10 = 270 ;

   Subtract "10" from each side of the equation;

       5x + 10 − 10 = 270 − 10 ;

to get:

      5x = 260 ;

Divide EACH SIDE of the equation by "5" ; 

      5x / 5 = 260 / 5  ; 

to get:

         x = 52 ;

x = 52 ;

x + 1   = 52 + 1 =  53 ;

x + 2  = 52 + 2 = 54 ;

x + 3  = 52 + 3 = 55 ;

x + 4  = 52 + 4 = 56 ;

The 5 (FIVE) consecutive integers are:  52, 53, 54, 55, and 56 .

Let us check our

  52 + 53 + 54 + 55 + 56 =?  270 ?

 52 + 53 = 105; 

 105 + 54 = 159 ;

 159 + 55 = 214 ;

 214 + 56 = 270 ;

→  52 + 53 + 54 + 55 + 56 =?  270 ?  Yes!

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