When rearranging and solving equations there is one major rule…whatever you do to one side you have to do to the other. You will be asked to solve an equation or to “make x the subject”. There’s a few methods you should follow (in order).

Pesky Square Roots Are A Pain. You Can Get Rid Of Them By Squaring Both Sides

Example: Make t the subject of the formula m = √(t + 5)

So square both sides

m² = t + 5

Take 5 from both sides

t = m² – 5

Kill Off Any Fractions

Just multiply both sides by the denominator

Example: 4a = 5/4

Multiply both sides by 4

16a = 5

Divide both sides by 16

a = 5/16

Multiply Out Any Brackets

See the Brackets topic page.

Collect The Letter You Want To Find On One Side

Example: x = 2y – 4x – 5

Get all the xs on the same side by adding 4x to both sides

5x = 2y – 5

It’s now easy to make x the subject by dividing by 5!

Divide Both Sides To Get X

Example: 9x = 81y – 45

Divide both sides by 9

x = 9y – 5

If You Are Left With A Square Just Take The Square Root Of Both Sides

BUT!! Make sure to add a + and – in front!

Example: x² = (3y – 10)

x = ±√(3y – 10)