Text
Unit F2 Section 4
Algebraic Manipulation

Sometimes a letter may appear twice in a formula, for example,

p =

This section is concerned with how to make the repeated letter the subject of the equation.

Worked Examples

1

Make x the subject of the formula

ax − c = 3x + b

First bring all the terms containing x to one side of the equation. Subtracting 3x gives

ax − 3x − c = b

Then adding c to both sides gives

ax − 3x = b + c

Factorising gives

x(a − 3) = b + c

Finally, dividing by (a − 3) gives

x =

2

Make x the subject of the formula

p =

First multiply both sides by w − x and expand the brackets.

p(w − x) = 2x

pw − px = 2x

Next take all the terms containing x to one side of the equation and factorise.

pw = 2x + px

pw = x(2 + p)

Finally, dividing by (2 + p) gives

= x
or
x =
3

Make x the subject of the formula

p =

Square both sides to give

p2 =

Multiply both sides by x to give

p2x = × x
= x + 4

Take x from both sides to give

p2x − x = x + 4 − x
= 4

Factorise

(p2 − 1)x = 4

Divide both sides by (p2 − 1) to give

x =

Exercises

Make x the subject of each of the following formulae.

(a)

2x + a = x − b

x =
(b)

ax − b = cx − d

x =
(c)

xa − 4 = bx − 5

x =
(d)

3x − 6 = 4a + 2x

x =
(e)

b − 2x = c − 5x

x =
(f)

a − bx = c − dx

x =
(g)

2(x + 1) = a − x

x =
(h)

4(x − a) = 3(a − x)

x =
(i)

p(x + 1) = q(x − 1)

x =
(j)

=

x =
(k)

= x + 1

x =
(l)

=

x =

Make x the subject of each of the following formulae.

(a)

P =

x =
(b)

P =

x =
(c)

Q =

x =
(d)

q2 =

x =
(e)

= a

x =
(f)

= 4

x =
(g)

p =

x =
(h)

w =

x =
(i)

w =

x =
(j)

p =

x =
(k)

p =

x =
(l)

g =

x =