Math Nerds... will you help me? #2?

Question

Find two consecutive odd integers whose product is one less than six times their sum.
Domain for the smallest: {1, 1, 11}

A.1, 1

B.1, 3 or 11, 13

C.11, 13

D.1, 1 or 11, 13

Answer 1

x = first integer
x+1 = second integer

x(x+1) = 6(x+x+1)-1

Answer 2

Consecutive odd integers are two apart, like 3 and 5. So set up your variables:
Smaller: x
Larger: x + 2

Your sentence gives this equation:
x(x + 2) = 6(x + x + 2) -1
Do the distributive properties:
x^2 + 2x = 6x + 6x + 12 -1
Combine like terms:
x^2 + 2x = 12x + 11
Since this is a quadratic equation, get a zero on one side by subtracting the 12x and the 11
x^2 - 10x -11 = 0
Factor into two binomials:
(x - 11)(x + 1 ) = 0
Set each binomial equal to zero to solve. You'll get
x = {11, -1}

When you add 2 to each answer, your numbers will be
11 and 13 for one answer, -1 and 1 for the other.

Since your domain doesn't have any negatives, 11 and 13 is your solution.

Answer 3

C. 11,13

Why?

When you multiply 11 and 13, you get 143.
If you add 11 and 13 you get 24.
24 multiplied by 6 equals 144.

AND 143 is one (1) less than 144.

Answer 4

B,because A and C are the same as D