This document provides examples and instructions for making x the subject of an equation. It includes two examples of solving equations: (1) finding the cost of fertilizer for n bags and how many bags can be bought for $110, and (2) finding the value of c when given values for a, b, and the equation. It then lists four steps for making x the subject of any formula: clear fractions, multiply out brackets involving x, put x-terms alone on one side, and divide by the coefficient of x. An example of applying the steps to the formula 2x + 3b = c is shown.

1. ALGEBRA
More examples and how to
make x the subject of the
equation.

2. EXAMPLE (1)
A farmer pays $20 per bag of fertiliser, plus a fixed delivery fee of $30.
(a) Find the cost of C, for n bags of fertiliser.
(b) How many bags can the farmer buy for $110?
(a) n bags at $20 per bags costs 20n
Delivery costs $30
Total cost C = 20n +30
(b) 110 = 20n + 30 subtract 30 from each side. (paso el 30 restando)
80 = 20n divide each side by 20. (paso el 20 dividiendo)
n = 4  the farmer can buy 4 bags for $110

3. EXAMPLE (2)
If 𝑫 =
(𝒂−𝒃) 𝟐
𝒄 𝟐 find the value of c when a=7, b=-2 and D=4.
4 =
(7−(−2))2
𝑐2 (paso el 4 dividiendo y la c multiplicando. Resuelvo lo que esta dentro de los () )
𝑐2 =
92
4
=
81
4
(paso el cuadrado como raíz cuadrada)
𝑐 =
2 81
4
=
9
2
= 4.5

4. TO MAKE X THE SUBJECT OF ANY FORMULA USE
THE FOLLOWING STEPS:
1. Clear the fractions
2. Multiply out any brackets involving x
3. Put x-terms together alone on one side of the formula
4. Divide both sides by coefficient of x-term.

5. EXAMPLE
Make x the subject of the formula: 𝟐𝒙 + 𝟑𝒃 = 𝒄
1. Clear the fractions  no fractions
2. Multiply out any brackets involving x  no brackets multiplying out
3. Put x-terms together on one side
2𝑥 = 𝑐 − 3𝑏
4. Divide coefficient of x-term  the coefficient of x-term is 2
𝑥 =
𝑐 − 3𝑏
2