Making X the Subject question on photo.?

1.
y = x / (x - 4)
y (x - 4) = x
yx - 4y = x
yx - x = 4y
x (y - 1) = 4y
x = 4y / (y - 1)


2.
y = (x + 3) / (x - 7)
y (x - 7) = x + 3
xy - 7y = x + 3
xy - x = 7y + 3
x (y - 1) = 7y + 3
x = (7y + 3) / (y - 1)


3.
y = (a - 6x) / (bx + 9)
y (bx + 9) = a - 6x
byx + 9y = a - 6x
byx + 6x = a - 9y
x (by + 6)= a - 9y
x = (a - 9y) / (by + 6)


4.
y = (8x - 12) / (9x - 15)
y (9x - 15) = 8x - 12
9yx - 15y = 8x - 12
9yx - 8x = 15y - 12
x (9y - 8) = 15y - 12
x = (15y - 12) / (9y - 8)


5.
(w / 3) + (2 / x) = 4
2 / x = 4 - (w / 3)
2 / x = (12 / 3) - (w / 3)
2 / x = (12 - w) / 3
x / 2 = 3 / (12 - w)
x = 6 / (12 - w)

Ahh, I suppose this is to train you to find the inverse functions, you should solve them by yourself, it is easy, I will solve two for you, the toughest one and you should get the idea, because you only learn math if you solve it by yourself.

The fifth one seems to be the toughest.
w / 3 + 2 / x = 4
2 / x = 4 - w / 3
2 / x = 12 / 3 - w / 3
2 / x = 12 - w / 3
x / 2 = 3 / 12 - w
x = 6 / 12 - w
Another tough one seems to be the third one, I will do it for you.

y= a -6 x / b x- 9
byx -9y = a - 6x
byx +6x= a- 9y
x(by + 6)= a- 9y
x= a- 9y/by +6

Please, solve the rest by yourself and do not try and copy and solve, I also received similar sums when I was in 5th Grade, and I copied it from my friend, which made me fail my class test as I only copied my homework, not solving it by myself.

(2) y(x-7) = x + 3 =>
x(y - 1) = 7y + 3 =>
x = (y-1)/(7y+3).

(3) y (bx + 9) = a - 6x =>
x (by + 6) = a - 9y =>
x = (a - 9y) / (by + 6).

(4) is pretty easy, just follow the same procedure I used in #2.

I agree with iceman's answers for 1 and 5

1)
yx - 4y = x
yx - x = 4y
x(y - 1) = 4y
x = (4y)/(y - 1)

5)
2/x = 4 - w/3
2/x = (12 - w)/3
x/2 = 3/(12 - w)
x = 6/(12 - w)

Edit: okay:

2)
yx - 7y = x + 3
yx - x = 7y + 3
x(y - 1) = 7y + 3
x = (7y + 3)/(y - 1)

3)
ybx + 9y = a - 6x
ybx + 6x = a - 9y
x(by + 6) = a - 9y
x = (a - 9y)/(by + 6)

4)
9xy - 15y = 8x - 12
9xy - 8x = 15y - 12
x(9y - 8) = 15y - 12
x = (15y - 12)/(9y - 8)

I hope this helps.

y = x/(x-4)

get rid of the fraction by multiplying both sides by (x-4):

(x-4)(y) = x(x-4)/(x-4)

y(x-4) = x

expand all terms

xy - 4y = x

now get all terms with x on one side and the rest on the other

xy - x - 4y = x - x

xy - x - 4y = 0

xy - x - 4y + 4y = 0 + 4y

xy - x = 4y

and now isolate x through factoring and then through division

x(y-1) = 4y

x(y-1) / (y-1) = 4y/(y-1)

x = 4y / (y-1)





y = (x+3) / (x-7)

multiply to get rid of the fraction

y(x-7) = (x+3)

expand all terms, collect x's on one side and the rest on the other

xy - 7y = x + 3

xy - x = 3 + 7y

x(y-1) = 7y + 3

x(y-1) / (y-1) = (7y+3) / (y-1)

x = (7y+3) / (y-1)




y = (a - 6x) / (bx+9)

y(bx+9) = (a-6x)

bxy + 9y = a - 6x

bxy + 6x = a - 9y

x (by + 6) = (a - 9y)

x = (a - 9y) / (by + 6)



the rest is all the same.