Algebra math Help, how to get it?

Question

please tell me the steps to get it..not just the answers ,Thanks!
it says to solve for x
1)
_x_+_1_ = _x_ = 2) x ^2 +10x + 21
3 2

3 is under X+1 and 2 is under the X
please help me on Two of them ..I know you can help me..Please..Thanks!

Answer 1

(x+1)/32 = x/2 first cross multiply

2(x+1)=32x

2x+2=32x
2=30x
2/30=x
1/15=x

Answer 2

(x+1)/3 = x/2

And x² + 10x +21


There are a bunch of ways to attack the first one
But if you multiply both sides of the equation by 6 you get
(6/3)(x+1)=(6/2)x Doing the arithmetic...
2(x+1)=3x
Multiplying the left side out
2x + 2 = 3x
Add a -2x to both sides
2 = x


I'm not certain what you want to do with the second problem.
x² + 10x +21 but my guess is that you want to factor it.

You are looking for factors that look like this:
(ax+b)(cx+d)
ac=1
bd=21
and ad+bc=10

First, you can almost bet that a=c=1 because ac=1. It's not always true, but if fractions exist in a,b,c,or d, you get strange looking fractions in the middle term.
Since a=c=1 then
ad+bc = (1)(d)+(1)(b) = d+b and we know that's 10

Looking at the factors for 21... 1 and 21, and 3 and 7.
These are the possible values for b and d. The only combination of factors that total 10 is 3 and 7.
So the factors have to look like
(x+3)(x+7)

You probably don't need to write down all these steps, but your head has to go through them.

Answer 3

the first thing is to remove the fractions from the equation and that is done by multiplying the entire equation by the lowest common demonator, which is 6 (3x2) so you have:

6(x/3+1)=6(x/2)
6x/3 +6=6x/2, now simplify
2x +6 =3x, gather like terms
6=x

2) The idea is to factor,.
x^2 +10x+21. How do you factor? It is somewhat of a puzzle to make the pieces fit. What times what = 21? 1 x 21 and 3x7. The factors need to add up to 10 when you add them together. 3+7=10, so our factor is
(x + 3) (x +7)
When you have a factoring problem, it is assumed that the factored equation equals 0 and when you multiply numbers together, at least one of the numbers needs to be 0 if you are going to get 0 as an answer, so you now have two possible solutions for x.
x+3=0 and x +7=0
x= -3 and x= -7

Answer 4

Question 1
(x + 1) / 3 + 1 = x / 2
2.(x + 1) + 6 = 3x
2x + 2 + 6 = 3x
8 = x

Question 2
x² + 10x + 21 = (x + 7).(x + 3)

Answer 5

X^2+10X+21 = 0
X^2+7X+3X+21 = 0
X(X+7)+3(X+7) = 0
(X+3) (X+7) = 0
X = -3 0r -7
------------------------------
(X+1)/3 = X/2
Cross Multiplying
2(X+1) = 3X
2X+2=3X
2 = 3X-2X
2=X
X= 2

Answer 6

can't read 1) ???
do you mean (x+1)/3 = x/2
???
SEE YOUR PREVIOUS POST.


If so, then clear fractions by multiplying by 6
6*(x+1)/3 = 6*(x/2)
2(x+1) = 3x ===> distribute 2 to both terms
2x+2 = 3x ===> subtract 2x both sides
x=2