The product of two consecutive integers is 5 more than three time the larger. What are the integers?

When calculating consecutive integers, the smaller number is x and the larger number is (x + 1).

So the equation you can use is x + (x + 1) = 5 + 3 (x + 1)

This is because the sum of the consecutive integers are equal to 5 more than 3 times the larger integer.

Now simplify:

x + (x + 1) = 5 + 3 (x + 1)

2x + 1 = 5 + 3 (x + 1)

2x + 1 = 5 + 3x + 3

2x + 1 = 3x + 8

Now isolate the variable:

2x + 1 = 3x + 8

Subtract 2x from both sides:

1 = x + 8

Subtract 8 from both side:

-7 = x

x = - 7

So the smaller number is - 7 and the larger number is - 6.

Now check your answer:

-7 + (-7 + 1) = 5 + 3 (-7 + 1)

-7 + (-6) = 5 + 3 (-7 + 1)

-7 + (-6) = 5 + 3 (-7 + 1)

-7 - 6 = 5 + 3 (-7 + 1)

-13 = 5 + 3 (-7 + 1)

-13 = 5 + 3 (-6)

-13 = 5 + (-18)

-13 = 5 - 18

-13 = - 13

This works!

So the integers are - 7 and - 6.