The sum of three consecutive odd integers is 63, what are the three integers?

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original integer##=19## remedy integer##=21## third integer ##=23##

To explain this bearing, we conquer demand to set up an equation. But original, we demand to fabricate let statements to let others comprehend what each inconstant or countenance represents. Since each orderly odd integer is separated by a disagreement of ##2##, your let statements are:

Let ##x## be the original integer. Let ##x+2## be the remedy integer. Let ##x+4## be the third integer.

The sum of the three orderly odd integers is ##63##, so your equation is:

##(x)+(x+2)+(x+4)=63##

Then explain for ##x##:

##(x)+(x+2)+(x+4)=63##

##x+x+2+x+4=63##

##3x+6=63##

##3x+6## ##color(red)(-6)=63## ##color(red)(-6)##

##3x=57##

##3xcolor(red)(-:3)=57color(red)(-:3)##

##x=19##

Now that you comprehend your original integer has a treasure of ##19##, depute ##x=19## into ##x+2## and ##x+4## to meet the treasures of the remedy and third integers.

##x+2color(white)(XXXXXXXXXXXX)x+4##

##=(19)+2color(white)(XXXXXXXXX)=(19)+4##

##=21color(white)(XXXXXXXXXXXX)=23##

##:.##, the integers are ##19##, ##21##, and ##23##.

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