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A. if a+b+c+d=d+e+f+g=g+h+i=,a=4
find d,g.

The answer for this problem “if a+b+c+d=d+e+f+g=g+h+i ,a=4; find d and g” is only an expression.

1.) Let’s assume that:
a+b+c+d = x
d+e+f+g = y
g+h+I = z
Therefore a+b+c+d=d+e+f+g=g+h+i is equivalent to x=y=z

Let’s take one of the answers of d and I hope you can solve the rest of the answers.

2.) Let’s subtract both sides by –d so that we get:
a+b+c = x-d from (a+b+c+d-d = x-d)

Why did I do this?
(*)The thing here is that our equation must always be equal even whatever we will do with it. To make it clearer, a direct example will be solve.
In our assumption: a+b+c+d = x, let’s try to set x with the value of 10 and d with value of 1.
From a+b+c+d = x, which is 10 = 10, we have
a+b+c = x-d, which is 9 = 9. This is assuming that a+b+c+d has a value of 10.

3.) After that, we will isolate the d. Doing this is just like doing the procedure of #2.
We then get a+b+c-x = -d.

4.) To get a positive value of d, we will multiply both sides by -1.
We get –a-b-c+x = d or d = x-a-b-c from -1(a+b+c-x) = (-d)-1
The answer is d = x-4-b-c, where 4 is a constant of variable a.

5. Checking the answer if it’s correct. We replace the variables a value.
a = 4, this is constant as given in the problem.
b = 3, c = 2, d = 1

So from a+b+c+d we get 4+3+2+1 = 10 and x is also 10. Therefore 10 = 10
We substitute the given to the answer which is
d = x-4-b-c, => 1 = 10-4-3-2, => 1 = 1

So the solution is:
1.) assume a+b+c+d = x
2.) subtract both sides with d (this is called transposition)
a+b+c = x-d
3.) subtract both sides with x
a+b+c-x = -d
4.) multiply both sides with -1
x-a-b-c = d

The answers:
for d:
d = x-4-b-c
d = y-e-f-g

for g:
g = y-d-e-f
g = z-h-i

Try and solve for the other solutions. Post here my mistakes and I would gladly try to explain it.

For the second question. I can't figure it out because