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find all sets of three consecutive multiples of 6 whose sum is between -6 and 50

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1 Answer

a multiple of 6 can be written as 6n, where n is any integer
three consecutive multiples of 6 would be 6n, 6(n+1), and 6(n+2)
-6<6n+6(n+1)+6(n+2)<50
-6<6n+6n+6+6n+12<50
-6<18n+18<50
-6-18<18n+18-18<50-18
-24<18n<32
-24/18<18n/18<32/18
-1 6/18<n<1 14/18
-1 1/3<n<1 7/9
n is an integer
therefore, n=-1, n=0, and n=1
if n=-1, then you have 6(-1), 6(-1+1), 6(-1+2), 6(-1), 6(0), 6(1), or -6, 0, 6
if n=0, then you have 6(0), 6(0+1), 6(0+2), 6(0), 6(1), 6(2), or 0, 6, 12
if n=1, then you have 6(1), 6(1+1), 6(1+2), 6(1), 6(2), 6(3), or 6, 12, 18
you can't have -12, -6, 0 because they add up to -18 which is less than -6
you can't have 12, 18, 24 because they add up to 54 which is greater than 50