<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>
Answer:
a=5, a=-2.5
Step-by-step explanation:
<em>Given:</em>
<em />
<em>Solution:</em>
<em />
<u><em>~Lenvy~</em></u>
Answer:
x = 2 and y = 1
Step-by-step explanation:
A) 5x+y=11
B) x - y = 1.
(Solving by substitution)
B) x - 1 = y
A) 5x + (x -1) = 11. 6x-1=11. 6x = 11+1
6x = 12
x = 12/2. x = 2
B. 2 - 1 = y. y = 1
Answer:
Explanation:
We have:
(
2
x
+
3
)
(
4
x
2
−
5
x
+
6
)
Now let's distribute this piece by piece:
(
2
x
)
(
4
x
2
)
=
8
x
3
(
2
x
)
(
−
5
x
)
=
−
10
x
2
(
2
x
)
(
6
)
=
12
x
(
3
)
(
4
x
2
)
=
12
x
2
(
3
)
(
−
5
x
)
=
−
15
x
(
3
)
(
6
)
=
18
And now we add them all up (I'm going to group terms in the adding):
8
x
3
−
10
x
2
+
12
x
2
+
12
x
−
15
x
+
18
And now simplify:
8
x
3
+
2
x
2
−
3
x
+
18Step-by-step explanation:
Answer:
The Answer is 400
Step-by-step explanation:
