Changing the Subject of a Formula (Subject in More Than One Term)
⭐ Higher Tier Content
Changing the subject of a formula becomes more challenging when the subject appears in more than one term. In these cases, the subject must first be collected into a single term before it can be isolated.
This usually involves factorising.
Understanding the Structure
When the subject appears more than once, it is often:
• added or subtracted in different terms
• multiplied by different numbers
The key strategy is to:
- Move all terms containing the subject to one side
- Factorise the subject
- Isolate the subject using division
Collecting the Subject into One Term
Consider the formula:
$$
y = 3x + 2x
$$
The subject \( x \) appears in two terms. Collect the like terms:
$$
y = 5x
$$
Now divide both sides by \( 5 \):
$$
x = \frac{y}{5}
$$
Changing the Subject by Factorising
Consider the formula:
$$
y = 2x + 7x
$$
First collect the terms involving \( x \):
$$
y = 9x
$$
Now divide by \( 9 \):
$$
x = \frac{y}{9}
$$
Subject on Both Sides of the Formula
Often, the subject appears on both sides of the equation.
For example:
$$
y = 5x + 3
$$
To make \( x \) the subject, first rearrange so all \( x \) terms are on one side:
$$
y - 3 = 5x
$$
Now divide by \( 5 \):
$$
x = \frac{y - 3}{5}
$$
Another example:
$$
A = 4x - x
$$
Collect the \( x \) terms:
$$
A = 3x
$$
So:
$$
x = \frac{A}{3}
$$
Changing the Subject When the Subject Is in a Bracket
Consider:
$$
y = 3(x + 2)
$$
First expand the bracket:
$$
y = 3x + 6
$$
Now rearrange:
$$
y - 6 = 3x
$$
Divide by \( 3 \):
$$
x = \frac{y - 6}{3}
$$
Key Points to Remember
Always bring all terms containing the subject onto one side.
Factorise to isolate the subject in a single term.
Use inverse operations carefully and step by step.
Changing the subject when it appears more than once relies on careful rearrangement and factorisation, and is a key skill for solving algebraic problems and working with formulae.