Changing the subject of the formula?

Question

I am still trying to get used to these type of equations, so if you could explain how you did it that would be really helpful.

1.) a+b=ac (a as the subject)
2.) pr-p=qr+q (q as the subject)
3.)pr-p=qr+q (r as the subject)
4.)p(q+r)=q (q as the subject)

Answer 1

just rearrange the equations so that everything with the subject in it is on one side and every thing else is on the other side, you can then factor out the subject and rearrange for the solution

1.)
a+b=ac
subtract a from both sides
b=ac - a
factorise a from the right side
b=a(c - 1)
divide both sides by (c - 1)
a = b/(c - 1)

4.)
p(q+r)=q
expand the left side
pq + pr = q
subtract pq from both sides
pr = q - pq
factorise q from the right side
pr = (1 - p)q
divide both sides by (1 - p)
q = pr/(1 - p)

questions 2) & 3) are similar
the answers are
2) q = (pr-p)/(r+1)
3) r = (p+q)/(p-q)
I leave them for you

.,.,..,.,.

Answer 2

Ok, for the first one:
1) a + b = ac
a = ac - b
a/a = c-b
but this gives 1, so I don't think this works...

2) pr - p = qr + q
2q = (pr - p)/r
q= (pr - p)/2r

3)pr - p = qr + q
pr - qr = q + p
r(p-q) = q + p
r = (q+p)/(p-q)

4) p(q+r) = q
q + r = q/p
q = q/p - r
q/q = 1/p - r
again like the first example, the q's cancel and you are left with 1...

Answer 3

1)a+b=ac
a-ac=-b
take a common
a(1-c)=-b
a=b/(1-c)

2)pr-p=qr+q
take q as common
q(r+1)=pr-p
q=(pr-p)/(r+1)

3)pr-p=qr+q
pr-qr=q+p
taking r as common
r(p-q)=p+q
r=(p+q)/(p-q)

4) p(q+r)=q
pq+pr=q
pq-q=-pr
taking q as common
q(p-1)=-pr
q=(-pr)/(p-1)

Answer 4

1) a+b= a(c)
1+2=1(3)
3=3
2) p(r)-p=q(r)+q
4(6)-4=5(6)+5
20=35= 35/20
3) p(r)-p=q(r)+q
4(6)-4=5(6)+5
20=35/20
4) p(q+r) = q
4(5+6)=5
20+24=5
44=5
44=5/44
a=1
b=2
c=3
p=4
q=5
r=6

Answer 5

1) Divide both sides by a then you get:
(a + b)/a = (a*c)/a.
On the left hand side you get a/a + b/a = b/a +1 &
on the right hand side you get c,
so b/a +1 = c,
so b/a = c - 1,
so a/b = 1 / (c - 1).
Then multiply both sides by b:
a = b / (c- 1). [ans].
(a is, in effect, 'trapped' & you have to work out a way to set it free!).

Answer 6

a+b=ac
a-ac=-b
a(1-c)=-b
a=(-b)/(1-c)

pr-p=qr+q
qr+r=pr-p
qr=pr-p-r
q=(pr-p-r)/r

Similarly you can solve the rest