<span>Let the 2 consecutive odd integers be represented by: "x" and "(x+2) _________________ The product of these two consecutive odd integers is: ________________ </span>→ <span>x*(x + 2); or, write as: x(x + 2) __________________ The sum </span>of these two consecutive odd integers is: <span>________________________________ </span>→ <span>x + (x + 2) = (2x + 2) _______________________________ The product of 2 conductive integers, "</span>x(x + 2)" , is 1 less than 4 times their sum, "(2x + 2)". <span>______________________________ </span>→ Write as: 4*(2x + 2) − 1 = x(x + 2) <span>________________________________ Note the distributive property of multiplication: _______________________________ </span>→ <span>a*(b + c) = ab + ac ; ________________________________ We have: ___________ </span>→ 4*(2x + 2) − 1 = x(x + 2) <span>_____________________________ </span> → 4*(2x + 2) = (4*2x) + (4*2) = 8x + 8 <span>____________________________________ On the "right side of the equation; we have: ______________________________________ </span>→ x(x + 2) = (x*x) + (x*2) = x² + 2x <span>_____________________________________ We can rewrite the equation: __________________________ </span>→ 4*(2x + 2) − 1 = x(x + 2) ; <span>___________________________ by substituting our obtained "expanded values" for: "[</span>4*(2x + 2)]" ; and for: "[x(x + 2)]" ; <span>______________________________________ </span>→ 4*(2x + 2) − 1 = x(x + 2) = ____________________________ → 8x + 8 − 1 = x² + 2x ; __________________________________ → Simplify the "+8 − 1" on the "left-hand side" of the equation to "7"; and subtract "2x" from EACH SIDE of the equation: <span>____________________________________ </span>→ 8x + 7 − 2x = x² + 2x − 2x ; to get: <span>____________________________ </span> → 6x + 7 = x² ; ________________________________ →To solve for "x"; Subtract "6x" and subtract "7"; from EACH SIDE of the equation; to get an equation in "quadratic format" ; that is: <span>_____________________________________________ ax
let x and x+2 be the consecutive odd integers.
Their product is x(x+2)
Their sum is x + x+2 or 2x+2
x(x+2)=4(2x+2)-1
Domain is odd integers</span>
