Question 980041
To solve, let's first find a way to represent the first integer and the second integer.  We'll use the letter a:


Integer 1:  a
Integer 2:  a + 2 (because 2 more than our first odd number will be the next consecutive odd number)


Next, let's convert our word problem into an equation.


"The product of two consecutive odd integers": (a)(a + 2) or a x (a+2)
"is": =
"1 less than 5 times their sum": 5(a + a + 2) - 1


Now, let's put it all together:  (a)(a + 2) = 5(a + a + 2) - 1, which is the equation we will use.


To solve for a (which is our first odd integer), first let's simplify each side of our equal sign:


(a)(a + 2) -----> {{{a^2+2a}}} and 5 (a + a + 2) - 1 -----> 5(2a + 2) - 1 -----> 10a + 10 - 1 -----> 10a + 9.  So, now we have:


{{{a^2+2a=10a+9}}}



Next, move everything on the right side of the equation to the left side of the equation and combine all like terms on the left side of the equation:


{{{a^2+2a-10a-9=0}}} -----> {{{a^2-8a-9=0}}}


Our next step is to factor {{{a^2-8a-9=0}}}, which will give us:


(a - 9)(a + 1) = 0


Set each set of parentheses equal to 0 to solve for a, which will give us two different values for a:


a - 9 = 0 -----> a = 9
a + 1 = 0 -----> a = -1


We now know that our first odd integer is both 9 and -1.  To find both of our second pair of odd integers, we will replace a in a + 2 with both 9 and -1:


a + 2 ----> 9 + 2 -----> 11
a + 2 -----> -1 + 2 -----> 1


So, when our first integer is 9, the next consecutive odd integer is 11, and when our first integer is -1, the next consecutive odd integer is 1.  In paired point form, with the lowest of the two integers first, our answer would be:


(-1, 1) and (9, 11)