document.write( "Question 94907: If the sum of the consecutive integers from -22 to x, inclusive, is 72, what is the value of x? \n" ); document.write( "

Algebra.Com's Answer #69453 by bucky(2189) $\"\"$ $\"About$

You can put this solution on YOUR website!
Think about this ...
\n" ); document.write( ".
\n" ); document.write( "If you start adding the numbers from -22 to zero, you are adding -22, - 21, - 20, -19 and
\n" ); document.write( "so on up to adding -3, then -2, then -1.
\n" ); document.write( ".
\n" ); document.write( "To this total you begin to add the numbers on the positive side of zero starting with +1,
\n" ); document.write( "then +2, +3 and so on....
\n" ); document.write( ".
\n" ); document.write( "When you think about it the -1 cancels the +1, the -2 cancels the +2, the -3 cancels the
\n" ); document.write( "+3 and so on until you get to -19 cancels +19, -20 cancels + 20, -21 cancels the +21, and
\n" ); document.write( "-22 cancels +22. So when you add all the integers from -22 to +22 the total is zero.
\n" ); document.write( ".
\n" ); document.write( "Starting at that point you next add +23 then +24 and then +25. The total of these three
\n" ); document.write( "integers is 72 as required by the problem.
\n" ); document.write( ".
\n" ); document.write( "So +25 is the last integer you need and, therefore, it is the x you are looking for.
\n" ); document.write( ".
\n" ); document.write( "Algebraically adding all the integers from -22 to +25 results in a total of +72.
\n" ); document.write( ".
\n" ); document.write( "Hope this gives you some insight into how you can solve this problem mostly by just thinking
\n" ); document.write( "about it logically.
\n" ); document.write( " \n" ); document.write( "

\n" );