1. Rearranging Equations

2. Things to remember:
Don’t rush it. You must go through each stage of your method and not try to skip any.
If you are making x the subject it means that you want to end up with x = and this is the only x in your answer.
Whatever you do to one side of the equals sign you must do to the other.

3. This means we want to rearrange the equation so it says
Rearrange the equation to make a the subject
b = 5a + 21
b – 21 = 5a
b – 21 = a
This means we want to rearrange the equation so it says
a =
÷5 ÷5 5
Our answer should say ... a = b – 21 5

4. This means we want to rearrange the equation so it says
Rearrange the equation to make t the subject
h = t
h – 13 = 7t
h – 13 = t
This means we want to rearrange the equation so it says
t =
÷7 ÷7 7
Our answer should say ... t = h – 13 7

5. Hint: You need to expand the brackets first
Exercise One
Rearrange each equation to make s the subject
u = 11s + 3
w = 8s + p
q = 3s + 4t
7s + m + t = l
a = 3(s + 4)
4 = g(s – 7)
22 + 5s = g
r = q – 3s
Hint: You need to expand the brackets first

6. Rearrange each equation to make s the subject
u = 11s + 3  s = u - 3
w = 8s + p  s = w – p
q = 3s + 4t  s = q – 4t
7s + m + t = l  s = l – m – t
a = 3(s + 4)  s = a – 12 = a - 4
4 = g(s – 7)  s = 4 + 7g = 4 + 7
22 + 5s = g  s = g - 22
r = q – 3s  s = q - r 11 8 3 7 3 3 g g 5 3

7. This means we want to rearrange the equation so it says
Rearrange the equation to make v the subject
e = 3v + t
5e = 3v + t
5e – t = 3v
5e – t = v
This means we want to rearrange the equation so it says
v = 5
x x5
- t t
÷ ÷3 3
Our answer should say ... v = 5e – t 3

8. This means we want to rearrange the equation so it says
Rearrange the equation to make p the subject
m = p + n
m - n = p
2(m – n) = p
This means we want to rearrange the equation so it says
p = 2
- n n 2
x x2
Our answer should say ... p = 2(m – n)

9. Example more difficult
Rearrange the equation a = x to make x the subject.
a = x +
Method -
ad = dx + cx
multiply both sides by d
dx + cx = ad
rearrange to get x’s on the left
x(d + c) = ad
factorise
x =
divide by (d + c)

10. Example more difficult
Rearrange the equation a = +
to make p the subject.
a = +
Method -
apq = q + p
multiply both sides by pq
apq – p = q
rearrange to get p’s on the left
p(aq – 1) = q
factorise
p =
divide by (aq – 1)

11. Example more difficult
Rearrange the equation a = b +
to make p the subject.
Method -
a = b +
a(1 + p) = b(1 + p) + c
multiply both sides by 1 + p
a + ap = b + bp + c
expand brackets
ap – bp = b + c – a
rearrange to get p’s on the left
p(a – b) = b + c – a
factorise
p =
divide by (a – b)

12. Example more difficult
Rearrange the equation s = b +
to make t the subject.
Method -
s = b +
s – b =
subtract b from both sides
(s – b)² =
square both sides
= (s – b)²
rearrange to get t on the left
multiply by p
t = p(s – b)²

13. Test Yourself 1. Rearrange the equation a = x + to make x the subject.
Check your answers on previous slides
Test Yourself
1. Rearrange the equation a = x to make x the subject.
2. Rearrange the equation a = +
to make p the subject.
3. Rearrange the equation a = b +
to make p the subject.
4. Rearrange the equation s = b +
to make t the subject.