Two sets of three consecutive integers have a property that the product of the larger two is
one less than 7 times the smallest. Set up and solve an equation that can be sue to find both
sets of integers. What are those sets of integers?

Set up an equation for the verbal description: the product (mulitplication) of the two larger integers (the last two) is one less than 7 times the smallest (the first one).

(n + 1)(n + 2) = 7n - 1

Multiply (FOIL) the left side.

n^2 + 3n + 2 = 7n - 1

Subtract 7n and subtract 1 to make the right side 0.

n^2 - 4n + 3 = 0

Factor.

(n - 1)(n - 3) = 0

Set the two factors equal to 0

n - 1 = 0, n - 3 = 0

Solve for n.

n = 1, n = 3

One set of integers begins with 1, so it's {1, 2, 3}.

The other set begins with 3, so it's {3, 4, 5}

Two sets of three consecutive integers have a property that the product of the larger two is one less than 7 times the smallest. Set up and solve an equation that can be sue to find both sets of integers. What are those sets of integers?

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Two sets of three consecutive integers have a property that the product of the larger two is
one less than 7 times the smallest. Set up and solve an equation that can be sue to find both
sets of integers. What are those sets of integers?