# Changing The Subject

## Change the subject in formulae in which the new subject appears twice.

##### Level 1Level 2Level 3Level 4Level 5Level 6Level 7Level 8ExamMenuHelpMore

Make $$x$$ the subject of each formula given below then drag the equivalent solution to the answer panel. There are spaces where you can show your working (see the Help tab for more information)

 $$ax-b=cx$$ $$ax+b=cx+d$$ $$a(x-b)=c(d-x)$$ $$a(3-x)=5x$$ $$a= \frac{cx - b}{x}$$ $$x+c=a-bx$$ $$a = \frac{bx}{x+c}$$ $$\frac{ax-c}{b+x} = d$$ $$a = \sqrt{ \frac{x+10}{x} }$$ $$\frac{5b}{2x} = \frac{c + b}{x-e}$$ $$( \frac{x^2 - 10}{x^2 + 10} )^2 = a$$ $$\frac{1}{x} ( \frac{ax}{c} +b) = 10d$$

$$x= \frac{b}{a-c}$$

$$x= \frac{d-b}{a-c}$$

$$x= \frac{ab+cd}{a+c}$$

$$x= \frac{3a}{a+5}$$

$$x= \frac{b}{c-a}$$

$$x= \frac{a-c}{b+1}$$

$$x= \frac{ac}{b-a}$$

$$x= \frac{db+c}{a-d}$$

$$x= \frac{10}{a^2-1}$$

$$x= \frac{5be}{3b-2c}$$

$$x= \sqrt{\frac{10(1+\sqrt{a})}{1-\sqrt{a}}}$$

$$x= \frac{bc}{10cd-a}$$

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This is Changing The Subject level 8. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Exam-style Questions

## Description of Levels

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Level 1 - Formulas which can be rearranged by adding or subtracting terms from both sides

Example: Make e the subject of the formula d = e - f

Level 2 - Formulas which can be rearranged by multiplying or dividing both sides by a value

Example: Rearrange the formula n = mp

Level 3 - Formulas which can be rearranged by adding, subtracting, multiplying or dividing both sides by a value

Example: Rearrange the formula b = a + cd

Level 4 - Formulas including brackets or expressions in the numerator or denominator of a fraction

Example: Rearrange the formula p = s(t + 2)

Level 5 - Formulas including squares or square roots

Example: Rearrange the formula d² = 2a + 1

Level 6 - Finding the unknown which is not the subject of a formula

Example: If m = n² + 2p, find p when m=8 and n=10

Level 7 - Rearrange the formulae where the new subject appears twice; fill in the blanks

Example: Rearrange the formula ax + b = cx + g to make x the subject

Level 8 - Rearrange the formulae where the new subject appears twice; show your working

Example: Rearrange the formula a(3-x)=5x to make x the subject

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## Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

## Example

Make $$x$$ the subject of the following formula:

$$a = \frac{b-x}{2x+c}$$

Multiply both sides of the equation by $$2x+c$$

$$2ax + ac = b-x$$

Add $$x$$ and subtract $$ac$$ from both sides

$$2ax + x = b - ac$$

Factorise the left side

$$x(2a + 1) = b - ac$$

Divide both sides by $$2a + 1$$

$$x= \frac{b - ac}{2a + 1}$$

In the boxes made available to show working the following formatting shortcuts may be useful.

Fractions: use the forward slash / (use brackets to group together multiple term numerators)

Indices: use the up arrow key ^ then type the index.

Square root: type \sqrt followed by a space

+ The blue button allows you to add extra lines of working.

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