the product of two consecutive even integers is 12 more than six times the smaller number

Answer 1

Even integers (and odd integers) are two numbers from each other.

So the first integer is "x" while the second integer would be "x+2"

Product means multiply.

product of two consecutive even integers: x(x+2)

is: your verb is almost always your equal sign

12 more than: +12

six times the smaller number: 6x (since x is the smaller number)

x (x + 2) = 6x + 12

x² + 2x = 6x + 12

subtract 6x and 12 from both sides so that it is equal to 0

x² - 4x - 12 = 0

factor

(x - 6) (x + 2) = 0

x - 6 = 0 OR x + 2 = 0

x=6 OR x=-2

Answer 2

b = a + 2

ab = 6a + 12

Substitute!

a(a + 2) = 6a + 12

a² + 2a = 6a + 12

a2 - 4a - 12 = 0

a² - 6a + 2a - 12 = 0

a(a - 6) + 2(a - 6) = 0

(a + 2)(a - 6) = 0

a + 2 = 0

a = -2

-2,0

a - 6 = 0

a = 6

6,8