Let's put this in terms of a system of equations. Let's call the numbers x and y, with x being the larger integer and y the smaller one. Since they are consecutive odd integers, we know that:
x = y + 2
The constraint is:
xy= 3(x+y) + 71 Simplify
xy = 3x + 3y + 71 Plug in (y+2) for x:
(y + 2) y = 3(y + 2) + 3y + 71 Simplify
y² + 2y = 3y + 6 + 3y + 71 Subtract 6y from both sides, add 71+6
y² -4y = 77
y² - 4y - 77 = 0
Factor:
(y - 11) (y+7) = 0
y = 11 or y=-7
When y = 11, x = 13, since x = y+2
Plug in to make sure:
xy = 3(x+y) + 71
11*13 = 3 (11 + 13) + 71
143 = 3 (24) + 71
143 = 72 + 71
143 = 143
Our values work!
Answer: 11, 13
The restriction for this is that x ≠ 4. This is because 4 - 4 = 0, and you cannot divide by zero.
An alternative way of writing this (interval notation) is (-∞, 4)U(4, <span>∞).
Hope this helps!</span>
(3y-5 + 2y)*2 = (5y-5)*2 = 10y-10
2x + 1
You can find that by switching the signs in the second set of parenthesis and then adding.
