# 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.