Question 315390
Consecutive integers are integers that follow one another. For instance, 1, 2, 3 are consecutive integers. So if 'x' is an integer, then x+1 is the next integer making x and x+1 consecutive integers.



So "when the smaller of two consecutive integers is added to two times the larger, the result is 32", this means that {{{x+2(x+1)=32}}}



{{{x+2(x+1)=32}}} Start with the given equation.



{{{x+2x+2=32}}} Distribute.



{{{3x+2=32}}} Combine like terms on the left side.



{{{3x=32-2}}} Subtract {{{2}}} from both sides.



{{{3x=30}}} Combine like terms on the right side.



{{{x=(30)/(3)}}} Divide both sides by {{{3}}} to isolate {{{x}}}.



{{{x=10}}} Reduce.



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Answer:


So the solution is {{{x=10}}} 



This means that the first integer is 10 and the next consecutive integer is 11.



Notice that 10+2*11=10+22=32 which verifies our answer.